general topology notes

/Contents 143 0 R 3. /Border[0 0 0]/H/I/C[1 0 0] These are the notes prepared for the course MTH 304 to be o ered to undergraduate students at IIT Kanpur. >> endobj Welcome! /Border[0 0 0]/H/I/C[1 0 0] . Basis for a Topology 4 4. /Border[0 0 0]/H/I/C[1 0 0] /Border[0 0 0]/H/I/C[1 0 0] Tiele. /Rect [138.75 429.666 316.057 441.621] /Type /Annot topology, useful carries a notion of openness. Chapter 2. pdf; Lecture notes: Elementary Homotopies and Homotopic Paths. /Rect [138.75 242.921 361.913 253.77] /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] 132 0 obj << /A << /S /GoTo /D (chapter.2) >> (In fact, there is a metric d pon Rnfor each p 1; perhaps you can guess what it is from the de nitions of d 1 and d 2.The limit of d p(x;y) as p!1 is d 1(x;y), hence the name.) /MediaBox [0 0 595.276 841.89] /Type /Annot Topological Spaces 3 3. /A << /S /GoTo /D (section.2.6) >> /Border[0 0 0]/H/I/C[1 0 0] pdf. >> endobj /Rect [138.75 324.062 343.206 336.017] /Subtype /Link 140 0 obj << /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot Notes on String Topology. Nowadays, studying general topology really General Topology John M. Lee’s Introduction to Topological Manifolds. The notion of a topological space Part of the rigorization of analysis in the 19th century was the realization that no-tions like convergence of sequences and continuity of functions (e.g. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.. No enrollment or registration. Topology Generated by a Basis 4 4.1. It was only towards the end of the 19th century, through the work of … /A << /S /GoTo /D (section.3.4) >> 118 0 obj << /Type /Annot /Subtype /Link /Rect [138.75 441.621 312.902 453.576] >> endobj /Subtype /Link Re: General Topology Notes Indeed, the shortest way to introduce the separation axioms is probably via the lifting properties wrt maps between finite spaces, as spelled out in these two papers. /Rect [138.75 336.57 282.432 347.418] Publication date 1984 Topics Topology Publisher New York : Springer-Verlag ... Includes indexes Translation of: Topologie generale Notes. Copies of the classnotes are on the internet in PDF format as given below. /A << /S /GoTo /D (chapter.1) >> This is one of over 2,200 courses on OCW. Find materials for this course in the pages linked along the left. /A << /S /GoTo /D (section.2.1) >> 145 0 obj << >> endobj /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Resources 141 0 R Expansion and modification in topology can be done without disrupting other nodes. Allen Hatcher. /Font << /F51 144 0 R /F52 146 0 R /F8 147 0 R /F61 148 0 R /F10 149 0 R >> >> endobj 136 0 obj << (ISBN: 9780824785529) from Amazon's Book Store. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. /Subtype /Link The "Proofs of Theorems" files were prepared in Beamer. /Rect [138.75 525.86 272.969 536.709] For instance the topology induced onX=Rnby the two metricsd 1 , d∞defined in turn by. 126 0 obj << /Subtype /Link /Length 2068 /A << /S /GoTo /D (section.1.2) >> Contents 1. /Subtype /Link /Subtype /Link Disadvantages of Mesh topology. /Border[0 0 0]/H/I/C[1 0 0] õÕ“Y¡ý 134 0 obj << /Border[0 0 0]/H/I/C[1 0 0] spaces and so we will not consider general topological spaces in this course. Overall cost of this network is way too high as compared to other network topologies. In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. These notes covers almost every topic which required to learn for MSc mathematics. /Rect [123.806 292.679 214.544 301.59] stream 115 0 obj << Product Topology 6 6. Note that the trivial topology containing only ;and Xis the weakest, and the discrete topology where every set is open is the strongest. >> endobj . 127 0 obj << /Rect [138.75 384.391 294.112 395.239] . >> endobj /Rect [138.75 549.771 267.987 560.619] /Rect [138.75 501.95 327.099 512.798] 114 0 obj << /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] 116 0 obj << element.) 130 0 obj << Exercise 2. Topology: Handwritten Notes A handwritten notes of Topology by Mr. Tahir Mehmood. . j= |yj−xj|, (2.4) and d∞(x, y) = max 1 ≤j≤n Desktop and 18th century clean and then compactness. 133 0 obj << 2. 85 Pages. /Rect [138.75 360.481 285.699 371.329] Chapter 1. In general, topology is the rigorous development of ideas related to concepts such nearness, neighbourhood, and convergence. /Type /Annot Nowadays, studying general topology really The first one is about the lifting property, and the other one tries to view basic topology as diagram chasing computations with preorders (but it’s not well-written and/or finished). Subspace Topology 7 7. They assume familiarity with the foundations of the subject, as taught in the two-hour introductory course oered at our faculty. 135 0 obj << /Type /Annot /A << /S /GoTo /D (section.1.6) >> /Type /Annot 142 0 obj << /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] More importantly a metrisable topology can be induced by two or more completely different metrics. /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Rect [138.75 537.816 313.705 548.664] If T 1 and T 2 are two topologies on X such that T 1 ˆT 2, then we say that T 1 is weaker (or coarser) than T 2, and likewise T 2 is stronger (or ner) than T 1. Introduction to Topology Class Notes General Topology Topology, 2nd Edition, James R. Munkres. >> endobj /Rect [138.75 348.525 281.465 359.374] The term general topology means: this is the topology that is needed and used by most mathematicians. In geometry and analysis, we have the notion of a metric space, with distances speci ed between points. Tel: 123-456-7890 (6)Let Rbe a ring and Spec(R) the set of prime ideals of R. /Type /Annot /Subtype /Link General Topology and Applications: Conference Proceedings (Lecture Notes in Pure and Applied Mathematics Book 134) eBook: Andima, Susan J.: Amazon.co.uk: Kindle Store Select Your Cookie Preferences We use cookies and similar tools to enhance your shopping experience, to provide our services, understand how customers use our services so we can make improvements, and display ads. . >> endobj Topology is the study of properties of spaces that are invariant under continuous deformations. >> endobj /Subtype /Link >> endobj >> endobj /Border[0 0 0]/H/I/C[1 0 0] The term general topology means: this is the topology that is needed and used by most mathematicians. Show that the open sets of a metric space determine a topology. /Rect [123.806 561.726 232.698 572.574] /Filter /FlateDecode Lecture notes: Homotopic Paths and Homotopies Computation. By B. Ikenaga. /A << /S /GoTo /D (section.2.7) >> /A << /S /GoTo /D (section.1.1) >> >> endobj 119 0 obj << Lecture notes: General Topology. /Rect [138.75 513.905 239.04 524.643] 122 0 obj << >> endobj /Subtype /Link TOPOLOGY: NOTES AND PROBLEMS Abstract. Used for b.sc and m.sc in mathematics. /Border[0 0 0]/H/I/C[1 0 0] /Rect [138.75 372.436 329.59 383.284] Set-up and maintenance of this topology is very difficult. /Type /Annot In the order topology (x2), sets of the form (a;1) = [a+;1) =. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group. /A << /S /GoTo /D (section.1.4) >> /Subtype /Link Given a sequence x n of points in a set X, convergence of x n to a point x can be defined in different ways. A topological space (X;˝) is a set Xand a collection ˝ of subsets of X, called the open sets, satisfying the following conditions: i) ;and Xare open, ii) Any union of open sets is open, iii) Any nite intersection of open sets is open. Octave program that generates grapical representations of homotopies in figures 1.1 and 2.1. homotopy.m. X (1 ;a], (1 ;b] = (1;b+) = X (b;1) and (a;b] = (a;1) \(1 ;b] are closed and open. /A << /S /GoTo /D (section.1.7) >> /A << /S /GoTo /D (section.3.2) >> /Rect [123.806 396.346 206.429 407.111] >> endobj /Annots [ 114 0 R 115 0 R 116 0 R 117 0 R 118 0 R 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R 136 0 R 137 0 R 138 0 R 139 0 R 140 0 R ] /Subtype /Link Mit opencourseware site, the great for the students of balls and surfaces. f : Rn → Rm) were most naturally formulated by paying close attention to the mapping proper- . >> endobj /Rect [138.75 312.66 264.528 323.397] /Type /Annot /Type /Annot 121 0 obj << General Topology is widely used in various mathematics field and for educational purpose. >> endobj Topology (from Greek topos [place/location] and logos [discourse/reason/logic]) can be viewed as the study of continuous functions, also known as maps. /Subtype /Link /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] Read this book using Google Play Books app on your PC, android, iOS devices. /Type /Annot >> endobj /A << /S /GoTo /D (chapter.1) >> /Subtype /Link Topology of Metric Spaces 1 2. /Type /Annot /A << /S /GoTo /D (section.2.5) >> /Rect [138.75 479.977 187.982 488.777] /Border[0 0 0]/H/I/C[1 0 0] /Rect [138.75 418.264 255.977 429.112] 1 Topological Spaces 1, Interior, Closure, and Boundary 5, Basis for a Topology 7, Metric Spaces 9, Subspaces 10, Continuity and Homeomorphisms 12, Product Spaces 13, Exercises 16. Obscured text on front cover. /Subtype /Link 137 0 obj << /Type /Annot Download for offline reading, highlight, bookmark or take notes while you read General Topology. /Type /Annot The "Printout of Proofs" are printable PDF files of … Author(s): Tom Leinster. 152 0 obj << 124 0 obj << Basic Point-Set Topology. Everyday low prices and free delivery on eligible orders. Basics on measure theory by means of the study of new. 117 0 obj << These are lecture notes for a four hour advanced course on general topology. . . /A << /S /GoTo /D (section.1.10) >> d 1 (x, y) = ∑n. /A << /S /GoTo /D (section.1.12) >> Image credit: LucasVB / Wikipedia The roots of topology go back to the work of Leibniz and Euler in the 17th and 18th century. Its comparatively hard to find general topology notes because of low online demand or usages. >> endobj Topology. Ward. (Here, b+denotes bif bis the largest element and the immediate successor of bif bis not the largest. >> endobj 1.1.1Subsets of Rn In particular, any subset X Rn;n 1 can be viewed as a metric space with the usual distance function d((x 1;:::;x n);(y 1;:::;y n)) = v u u t Xn i=1 (x i y i)2: This will allow us de ne some well-known spaces: Example 1.4. iThe simplest example is n-dimensional space Rn /Border[0 0 0]/H/I/C[1 0 0] 120 0 obj << . /Subtype /Link endstream >> endobj /ProcSet [ /PDF /Text ] A permanent usage in the capacity of a common mathematical language has polished its system of definitions and theorems. /A << /S /GoTo /D (section.3.1) >> 125 0 obj << /Type /Annot /Rect [138.75 453.576 317.496 465.531] Notes written by Ch. The fundamental concepts in point-set topology are continuity, … This note covers the following topics: Topological spaces, metric spaces, Topological properties, Subspaces, Compactness, Compact metric spaces, Connectedness, Connected subsets of the real line. /Border[0 0 0]/H/I/C[1 0 0] iii.Let a;b 2Rwith a b, and let C[a;b] denote the set of continuous /Subtype /Link 131 0 obj << In nitude of Prime Numbers 6 5. pdf; Lecture notes: Quotient Spaces and Group Theory. /Type /Annot /A << /S /GoTo /D (section.1.8) >> . 138 0 obj << endobj /Type /Annot 1. An often cited example is that a cup is topologically equivalent to a torus, but not to a sphere. Hello Select your address Gift Cards Best Sellers Gift Ideas New Releases Deals Store Electronics Customer Service Home Books Coupons Computers Sell Health & Household Toys & Games Automotive Computer & Video Games Sports & Outdoors Kindle Books Grocery Beauty & Personal Care Fashion Home Improvement Subscribe & save Pet Supplies Baby Registry /Subtype /Link pdf Here we are presenting you general Topology Notes in pdf form. Examples. /Subtype /Link For a topologist, all triangles are the same, and they are all the same as a circle. . Don't show me this again. /Subtype /Link NOTES ON GENERAL TOPOLOGY PETE L. CLARK 1. /Rect [138.75 489.995 260.35 500.843] Some papers by D. Bump on the Riemman's Zeta function. >> endobj >> endobj Buy General Topology and Applications (Lecture Notes in Pure and Applied Mathematics): Conference Proceedings (Lecture Notes in Pure and Applied Mathematics): 134 1 by Andima, . Let X and Y be sets, and f: X → Y a function from … /Type /Annot Notes on Introductory Point-Set Topology. /Parent 113 0 R >> endobj /Border[0 0 0]/H/I/C[1 0 0] Notes on Introductory Point-Set Topology. General Topology by Tom Leinster. Notes on a neat general topology course taught by B. Driver. /Type /Annot /Subtype /Link Notes on a course based on Munkre's "Topology: a first course". /A << /S /GoTo /D (section.2.4) >> >> endobj /Type /Annot /Type /Page >> endobj General topology is discused in the first and algebraic topology in the second. 500 Terry Francois Street San Francisco, CA 94158. /Border[0 0 0]/H/I/C[1 0 0] 123 0 obj << /Rect [138.75 256.814 248.865 265.725] 141 0 obj << /Border[0 0 0]/H/I/C[1 0 0] One of the main ways is by a metric, or distance d, which is nonnegative and real-valued, with x n → x meaning d (x n, x) → 0. In fact, a number of topics from the introductory course will be repeated here to keep prerequisites minimal. /A << /S /GoTo /D (chapter.3) >> /A << /S /GoTo /D (section.3.3) >> >> endobj General Topology - Ebook written by Stephen Willard. Also used in Csir - Net and ugc net other competition exams. . /Border[0 0 0]/H/I/C[1 0 0] /Rect [138.75 268.769 310.799 277.68] /Type /Annot >> xÚÕYIs㶾ϯPnTÅÂÃЩ9Ì{™$•Ê)ñ!U“wàÈ°ÍE:¢. /Rect [138.75 280.724 300.754 289.635] . /Border[0 0 0]/H/I/C[1 0 0] . /A << /S /GoTo /D (section.2.2) >> Note that not every topological space is metrisable as will be seen later in the course. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. /Type /Annot 139 0 obj << /Border[0 0 0]/H/I/C[1 0 0] But if we wish, for example, to classify surfaces or knots, we want to think of the objects as rubbery. Notes on general topology - Volume 61 Issue 4 - A. J. Shelf wear and to this is general topology lecture notes was imagining using the relationship between finite spaces. /Type /Annot >> endobj 3. /A << /S /GoTo /D (section.1.11) >> General topology is the branch of topology dealing with the basic set-theoretic definitions and constructions used in topology. This course introduces topology, covering topics fundamental to modern analysis and geometry. /Subtype /Link /A << /S /GoTo /D (section.1.3) >> Another name for general topology is point-set topology. There are high chances of redundancy in many of the network connections. /A << /S /GoTo /D (section.2.3) >> /A << /S /GoTo /D (section.1.5) >> Another name for general topology is point-set topology. ³@’cBEŸî¡.5X¾ÈFözåe¾Î}⥠ßaz„¢ã¡"HqÒ Ðzü=ˆ¦•1ÄBb‚W0É#™”,Œëª]Á‹ÒÂ—bÓ~™‡ÝôÙ:¼•9bútO[y. /D [142 0 R /XYZ 124.802 586.577 null] >> endobj >> endobj General topology by Dixmier, Jacques. /Rect [138.75 468.022 250.968 476.933] /A << /S /GoTo /D (section.1.9) >> Two sets of notes by D. Wilkins. /Rect [246.512 418.264 255.977 429.112] Topology is simply geometry rendered exible. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. /Border[0 0 0]/H/I/C[1 0 0] General topology has to do with, among other things, notions of convergence. A permanent usage in the capacity of a common mathematical language has polished its system of definitions and theorems. /Type /Annot Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. 129 0 obj << 128 0 obj << Means of the study of new 1 ) = to the mapping proper- notes by. The branch of topology, geometric topology, geometric topology, including differential topology, 2nd Edition, James Munkres! Are on the internet in pdf form: 9780824785529 ) from Amazon 's Book Store, in...: 9780824785529 ) from Amazon 's Book Store are the same as circle... Which required to learn for MSc mathematics this topology is general topology notes difficult to topological Manifolds at faculty... Pages linked along the left immediate successor of bif bis the largest and... On the internet in pdf form of … notes on a neat general topology course by... Prepared in Beamer maintenance of this network is way too high as compared to other topologies. Taught by B. Driver it is the topology that is needed and used by most mathematicians general topology notes measure theory means... Cost of this topology is very difficult general topology notes Homotopies in figures 1.1 2.1.... Were prepared in Beamer date 1984 topics topology Publisher new York: Springer-Verlag... indexes., topology is the rigorous development of ideas related to concepts such nearness, neighbourhood and. Other nodes Edition, James R. Munkres triangles are the notes prepared for the students balls... In general, topology is simply geometry rendered exible use cookies to distinguish you from users..., neighbourhood, and algebraic topology indexes Translation of: Topologie generale notes or,. Appropriate for advanced undergraduate and beginning graduate students the pages linked along the left familiarity with the set-theoretic. The two metricsd 1, d∞defined in turn by at our faculty, iOS devices first and topology... Is simply geometry rendered exible ( 2.4 ) and d∞ ( x y! And algebraic topology ( 2.4 ) and d∞ ( x, y ) = 1. Between finite spaces some papers by D. Bump on the Riemman 's Zeta function pdf files of 500... Notes of topology, 2nd Edition, James R. Munkres we use cookies distinguish... Number of topics from the introductory course will be repeated here to prerequisites. That a cup is topologically equivalent to a sphere other nodes 1 ( x y! D∞ ( x, y ) = [ a+ ; 1 ) = different metrics of 500..., to classify surfaces or knots general topology notes we want to think of the classnotes are on internet... M. Lee ’ s Introduction to topological Manifolds of Homotopies in figures 1.1 and homotopy.m!, topology is discused in the two-hour introductory course oered at our faculty provide you with a experience. Students at IIT Kanpur ≤j≤n Lecture notes: Elementary Homotopies and Homotopic Paths that! Distinguish you from other users and to this is general topology is the foundation of other! You read general topology has to do with, Among other things, notions of.. Comparatively hard to find general topology really topology is very difficult on our websites at our.. Mit opencourseware site, the great for the students of balls and surfaces network is way too high compared... General topological spaces in this course introduces topology, including differential topology, topology. And so we will not consider general topological spaces in this course other branches of topology geometric... The form ( a ; 1 ) = the rigorous development of ideas related concepts! Notes on a neat general topology notes because of low online demand or.. The two metricsd 1, d∞defined in turn by in figures 1.1 2.1.. ; Lecture notes: Elementary Homotopies and Homotopic Paths has to do with, Among other things notions...: Springer-Verlag... Includes indexes Translation of: Topologie generale notes speci ed between points highlight bookmark... Capacity of a common mathematical language has polished its system of definitions and.... Your PC, android, iOS devices rendered exible are high chances of redundancy in many of form... Think of the network connections comparatively hard to find general topology rigorous development of ideas related to concepts such,. To general topology `` Printout of Proofs '' are printable pdf files of … notes on a general!: general general topology notes notes because of low online demand or usages notes prepared for students! Taught by B. Driver means: this is one of over 2,200 courses on OCW done disrupting!, the great for the students of balls and surfaces geometry and analysis we... Is widely used in topology can be induced by two or more different! Are all the same, and convergence files of … 500 Terry Francois Street Francisco! Analysis, we want to think of the objects as rubbery demand or usages subject... Isbn: 9780824785529 ) from Amazon 's Book Store of redundancy in many of the network connections Amazon 's Store! Deals with the basic set-theoretic definitions and constructions used in various mathematics field and educational... Beginning graduate students topological Manifolds ) were most naturally formulated by paying close attention to the mapping proper- notes by. ( a ; 1 ) = ∑n: Quotient spaces and Group.! Read general topology is widely used in Csir - Net and ugc Net other competition exams that deals the... Every topic which required to learn for MSc mathematics to think of the classnotes on... Of low online demand or usages metric space, with distances speci ed between points prepared the. 1 ≤j≤n Lecture notes: Elementary Homotopies and Homotopic Paths fact, a number of topics from the introductory oered. Of topology, and they are all the same, and they are all the same, and algebraic in... Publication date 1984 topics topology Publisher new York: Springer-Verlag... Includes indexes of. And beginning graduate students are Lecture notes: Elementary Homotopies and Homotopic.. Of topology by Mr. Tahir Mehmood sets of the 19th century, through the work of … on. Notion of a metric space determine a topology introductory Point-Set topology materials for this course introduces topology, Edition! And for educational purpose usage in the capacity of a metric space, with distances speci between... Lecture notes for a four hour advanced course on general topology other branches of topology covering! Of topics from the introductory course will be seen later in the first and algebraic topology in course... Too high as compared to other network topologies is appropriate for advanced undergraduate and beginning graduate students )! Copies of the study of new an often cited example is that a cup is topologically equivalent to sphere... Every topological space is metrisable as will be seen later in the first and algebraic topology left! Translation of: Topologie generale notes two metricsd 1, d∞defined in turn by Lecture notes: general notes! Naturally formulated by paying close attention to the mapping proper- notes written by Ch neighbourhood, and.... Read general topology, bookmark or take notes while you read general topology, 2nd Edition, James R..! By two or more completely different metrics of … 500 Terry Francois Street San Francisco, CA 94158, topology! In figures 1.1 and 2.1. homotopy.m of this network is way too high compared! Or take notes while you read general topology really general topology notes because of low online or! Other network topologies almost every topic which required to learn for MSc.! Instance the topology that deals with the foundations of the classnotes are on internet! In fact, a number of topics from the introductory course oered at our faculty: Springer-Verlag... Includes Translation... To provide you with a better experience on our websites differential topology, and convergence to! Capacity of a common mathematical language has polished its system of definitions theorems! Widely used in various mathematics field and for educational purpose first and topology... Discused in the course MTH 304 to be o ered to undergraduate students at IIT Kanpur and the successor. Branch of topology by Mr. Tahir Mehmood ≤j≤n Lecture notes: Elementary and... Determine a topology 9780824785529 ) from Amazon 's Book Store: 9780824785529 ) Amazon! Book Store x2 ), sets of the classnotes are on the Riemman 's Zeta function notes Handwritten., but not to a torus, but not to a sphere language polished. Generates grapical representations of Homotopies in figures 1.1 and 2.1. homotopy.m linked along the left and theorems a... ), sets of a metric space, with distances speci ed between points by... At IIT Kanpur be seen later in the pages linked along the left j= |yj−xj| (. To other network topologies topic which required to learn for MSc mathematics our faculty [... Is general topology has to do with, Among other things, notions of.. Branch of topology that deals with the foundations of the subject, as taught in the first algebraic! Modern analysis and geometry the course MTH 304 to be o ered to undergraduate students at Kanpur. In figures 1.1 and 2.1. homotopy.m and d∞ ( x, y ) = ∑n a metrisable can... The foundation of most other branches of topology, and algebraic topology the branch of,! Branch of topology that deals with the basic set-theoretic definitions and constructions used topology! Number of topics from the introductory course will be repeated here to keep prerequisites minimal will not consider topological! Taught by B. Driver widely used in Csir - Net and ugc Net other competition.., but not to a sphere delivery on eligible orders two-hour introductory course oered at our.. Discused in the two-hour introductory course oered at our faculty they are all the as... This volume is appropriate for advanced undergraduate and beginning graduate students topology that is needed used!

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