Topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; London ; Sydney ; Toronto
Allyn and Bacon
[1966]
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| Series: | Allyn and Bacon series in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xvi, 447 Seiten |
| ISBN: | 0205002714 |
Staff View
MARC
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| 100 | 1 | |a Dugundji, James |d 1919-1985 |0 (DE-588)17205768X |4 aut | |
| 245 | 1 | 0 | |a Topology |c James Dugundji, Professor of Mathematics, University of Southern California, Los Angeles |
| 264 | 1 | |a Boston ; London ; Sydney ; Toronto |b Allyn and Bacon |c [1966] | |
| 264 | 4 | |c © 1966 | |
| 300 | |a xvi, 447 Seiten | ||
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| 650 | 4 | |a Topologie | |
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Record in the Search Index
| _version_ | 1804115381610086400 |
|---|---|
| adam_text | Co nt ent s I. Elementary Set Theory 1 2 3 4 5 6 7 8 9 II. I Sets Boolean Algebra Cartesian Product Families of Sets Power Set Functions, or Maps Binary Relations;Equivalence Relations Axiomàtics General CartesianProducts Problems Ordinals and Cardinals 1 2 3 4 5 6 7 8 9 1 3 7 8 10 10 14 17 21 25 29 Orderings Zorn’s Lemma; Zermelo’s Theorem Ordinals Comparability of Ordinals Transfinite Induction and Construction Ordinal Numbers Cardinals Cardinal Arithmetic The Ordinal Number Ω Problems ix 29 31 36 38 40 41 45 49 54 57
x III. Contents Topological Spaces 1 Topological Spaces 2 Basis for a Given Topology 3 Topologizing of Sets 4 Elementary Concepts 5 Topologizing with Preassigned Elementary Opera tions 6 G6, Fa, and Borei Sets 7 Relativization 8 Continuous Maps 9 Piecewise Definition of Maps 10 Continuous Maps into E1 11 Open Maps and Closed Maps 12 Homeomorphism Problems IV. Cartesian Products 1 Cartesian Product Topology 2 Continuity of Maps 3 Slices in Cartesian Products 4 Peano Curves Problems V. Connectedness 1 Connectedness 2 Applications 3 Components 4 Local Connectedness 5 Path-Connectedness Problems VI. Identification Topology; Weak Topology 1 Identification Topology 2 Subspaces 3 General Theorems 4 Spaces with Equivalence Relations 5 Cones and Suspensions 62 62 64 65 68 72 74 77 78 81 83 86 87 90 98 98 101 103 104 105 107 107 110 111 113 114 116 120 120 122 123 125 126
Contents xi 6 7 8 VII. Attaching of Spaces The Relation K(f)for Continuous Maps Weak Topologies Problems Separation Axioms 1 Hausdorff Spaces 2 Regular Spaces 3 Normal Spaces 4 Urysohn’s Characterization of Normality 5 Tietze’s Characterization of Normality 6 Covering Characterization of Normality 7 Completely Regular Spaces Problems VIII. Covering Axioms 1 Coverings of Spaces 2 Paracompact Spaces 3 Types of Refinements 4 Partitions of Unity 5 Complexes; Nerves of Coverings 6 Second-countable Spaces;Lindelöf Spaces 7 Separability Problems IX. Metric Spaces 1 Metrics on Sets 2 Topology Induced by a Metric 3 Equivalent Metrics 4 Continuity of the Distance 5 Properties of Metric Topologies 6 Maps of Metric Spaces into Affine Spaces 7 Cartesian Products of Metric Spaces 8 The Space Z2(j/); Hilbert Cube 9 Metrization of Topological Spaces 127 129 131 133 137 137 141 144 146 149 152 153 156 160 160 162 167 169 171 173 175 177 181 181 182 184 184 185 187 189 191 193
xii Contents 10 Gauge Spaces 11 Uniform Spaces Problems X. Convergence 1 Sequences and Nets 2 Filterbases in Spaces 3 Convergence Properties of Filterbases 4 Closure in Terms of Filterbases 5 Continuity; Convergence in CartesianProducts 6 Adequacy of Sequences 7 Maximal Filterbases Problems XI. Compactness 1 Compact Spaces 2 Special Properties of Compact Spaces 3 Countable Compactness 4 Compactness in Metric Spaces 5 Perfect Maps 6 Local Compactness 7 σ-Compact Spaces 8 Compactification 9 к-Spaces 10 Baire Spaces; Category Problems XII. Function Spaces 1 2 3 4 5 6 7 8 9 10 The Compact-open Topology Continuity of Composition; the Evaluation Map Cartesian Products Application to Identification Topologies Basis for ZY Compact Subsets of ZY Sequential Convergence in the c-Topology Metric Topologies; Relation to the c-Topology Pointwise Convergence Comparison of Topologies in ZY Problems 198 200 204 209 209 211 213 215 215 217 218 220 222 222 226 228 233 235 237 240 242 247 249 251 257 257 259 260 262 263 265 267 269 272 274 275
Contents xiii Xlil. The Spaces C(Y) 278 1 Continuity of the Algebraic Operations 2 Algebras in Č{ Y ; c) 3 Stone-Weierstrass Theorem 4 The Metric Space C(Y) 5 Embedding of Y in C( Y) 6 The Ring d(Y) Problems XIV. Complete Spaces 1 Cauchy Sequences 2 Complete Metrics and Complete Spaces 3 Cauchy Filterbases; Total Boundedness 4 Baire’s Theorem for Complete Metric Spaces 5 Extension of Uniformly Continuous Maps 6 Completion of a Metric Space 7 Fixed-Point Theorem for Complete Spaces 8 Complete Subspaces of Complete Spaces 9 Complete Gauge Structures Problems XV. Homotopy 1 Homotopy 2 Homotopy Classes 3 Homotopy and Function Spaces 4 Relative Homotopy 5 Retracts and Extendability 6 Deformation Retraction and Homotopy 7 Homotopy and Extendability 8 Applications Problems XVI. Maps into Spheres 1 Degree of a Map Sn — Sn 2 Brouwer’s Theorem 3 Further Applications of the Degree of aMap 4 Maps of Spheres into Sn 278 279 281 284 285 287 290 292 292 293 296 299 302 304 305 307 309 312 315 315 317 319 321 322 323 326 330 332 335 335 340 341 343
Contents XIV 5 6 7 XVII. Maps of Spaces into Sn Borsuk’s Antipodal Theorem Degree and Homotopy Problems Topology of En 1 Components of Compact Sets in En+1 2 Borsuk’s Separation Theorem 3 Domain Invariance 4 Deformations of Subsets of En+1 5 The Jordan Curve Theorem Problems XVIII. Homotopy Type 1 Homotopy Type 2 Homotopy-Type Invariants 3 Homotopy of Pairs 4 Mapping Cylinder 5 Properties of X in C(/) 6 Change of Bases in C(f) Problems XIX. Path Spaces; H-Spaces 1 2 3 4 5 6 7 8 XX. Path Spaces //-Structures //-Homomorphisms //-Spaces Units Inversion Associativity Path Spaces on //-Spaces Problems Fiber Spaces 1 2 Fiber Spaces Fiber Spaces for the Class of All Spaces 346 347 350 353 355 356 357 358 359 361 363 365 365 367 368 368 371 372 374 376 376 379 381 383 384 386 387 388 390 392 392 395
Contents XV 3 4 The Uniformization Theorem of Hurewicz Locally Trivial Fiber Structures Problems 399 404 408 Appendix One : Vector Spaces; Polytopes 410 Appendix Two : Direct and Inverse Limits 420 Index 437
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| any_adam_object | 1 |
| author | Dugundji, James 1919-1985 |
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| dewey-full | 513.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 513 - Arithmetic |
| dewey-raw | 513.83 |
| dewey-search | 513.83 |
| dewey-sort | 3513.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV000951727 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:21:43Z |
| institution | BVB |
| isbn | 0205002714 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000580495 |
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| owner_facet | DE-19 DE-BY-UBM DE-29T DE-83 DE-739 |
| physical | xvi, 447 Seiten |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Allyn and Bacon |
| record_format | marc |
| series2 | Allyn and Bacon series in advanced mathematics |
| spelling | Dugundji, James 1919-1985 (DE-588)17205768X aut Topology James Dugundji, Professor of Mathematics, University of Southern California, Los Angeles Boston ; London ; Sydney ; Toronto Allyn and Bacon [1966] © 1966 xvi, 447 Seiten txt rdacontent n rdamedia nc rdacarrier Allyn and Bacon series in advanced mathematics Hier auch später erschienene, unveränderte Nachdrucke Topologie Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000580495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dugundji, James 1919-1985 Topology Topologie Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Topology |
| title_auth | Topology |
| title_exact_search | Topology |
| title_full | Topology James Dugundji, Professor of Mathematics, University of Southern California, Los Angeles |
| title_fullStr | Topology James Dugundji, Professor of Mathematics, University of Southern California, Los Angeles |
| title_full_unstemmed | Topology James Dugundji, Professor of Mathematics, University of Southern California, Los Angeles |
| title_short | Topology |
| title_sort | topology |
| topic | Topologie Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie Topology |
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