General topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Polish |
| Veröffentlicht: |
Berlin
Heldermann
1989
|
| Ausgabe: | Rev. and completed ed. |
| Schriftenreihe: | Sigma series in pure mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 529 S. graph. Darst. |
| ISBN: | 3885380064 |
Internformat
MARC
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| 245 | 1 | 0 | |a General topology |c Ryszard Engelking |
| 250 | |a Rev. and completed ed. | ||
| 264 | 1 | |a Berlin |b Heldermann |c 1989 | |
| 300 | |a VIII, 529 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Sigma series in pure mathematics |v 6 | |
| 650 | 4 | |a Dimension | |
| 650 | 4 | |a Espace uniforme | |
| 650 | 4 | |a Exercice topologie | |
| 650 | 4 | |a Proximité | |
| 650 | 4 | |a Topologie générale | |
| 650 | 7 | |a Topologie |2 gtt | |
| 650 | 7 | |a Topologie |2 ram | |
| 650 | 4 | |a Topology | |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Sigma series in pure mathematics |v 6 |w (DE-604)BV000012120 |9 6 | |
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Datensatz im Suchindex
| _version_ | 1804120845377863680 |
|---|---|
| adam_text | Contents
Preface to the first edition vii
Preface to the revised edition viii
Introduction
1.1 Algebra of sets. Functions 1
1.2 Cardinal numbers 3
1.3 Order relations. Ordinal numbers 4
1.4 The axiom of choice 8
1.5 Real numbers 10
Chapter 1: Topological spaces
1.1 Topological spaces. Open and closed sets. Bases. Closure and interior of a set . . 11
1.2 Methods of generating topologies 20
1.3 Boundary of a set and derived set. Dense and nowhere dense sets. Borel sets ... 24
1.4 Continuous mappings. Closed and open mappings. Homeomorphisms 27
1.5 Axioms of separation 36
1.6 Convergence in topological spaces: Nets and filters. Sequential and Frechet spaces 49
1.7 Problems 56
Chapter 2: Operations on topological spaces
2.1 Subspaces 65
2.2 Sums 74
2.3 Cartesian products 77
2.4 Quotient spaces and quotient mappings 90
2.5 Limits of inverse systems 98
2.6 Function spaces I: The topology of uniform convergence on Rx and
the topology of pointwise convergence 105
2.7 Problems 112
Chapter 3: Compact spaces
3.1 Compact spaces 123
3.2 Operations on compact spaces 136
3.3 Locally compact spaces and fc spaces 148
3.4 Function spaces II: The compact open topology 156
3.5 Compactifications 166
3.6 The Cech Stone compactification and the Wallman extension 172
3.7 Perfect mappings 182
3.8 Lindelof spaces 192
3.9 Cech complete spaces 196
3.10 Countably compact spaces, pseudocompact spaces and
sequentially compact spaces 202
3.11 Realcompact spaces 214
3.12 Problems 220
vi
Chapter 4: Metric and metrizable spaces
4.1 Metric and metrizable spaces 248
4.2 Operations on metrizable spaces 258
4.3 Totally bounded and complete metric spaces. Compactness in metric spaces . . . 266
4.4 Metrization theorems I 280
4.5 Problems 288
Chapter 5: Paracompact spaces
5.1 Paracompact spaces 299
5.2 Countably paracompact spaces 316
5.3 Weakly and strongly paracompact spaces 322
5.4 Metrization theorems II 329
5.5 Problems 337
Chapter 6: Connected spaces
6.1 Connected spaces 352
6.2 Various kinds of disconnectedness 360
6.3 Problems 372
Chapter 7: Dimension of topological spaces
7.1 Definitions and basic properties of dimensions ind, Ind, and dim 383
7.2 Further properties of the dimension dim 394
7.3 Dimension of metrizable spaces 402
7.4 Problems 418
Chapter 8: Uniform spaces and proximity spaces
8.1 Uniformities and uniform spaces 426
8.2 Operations on uniform spaces 438
8.3 Totally bounded and complete uniform spaces. Compactness in uniform spaces . 444
8.4 Proximities and proximity spaces 451
8.5 Problems 460
Bibliography 469
Tables
Relations between main classes of topological spaces 508
Invariants of operations 509
Invariants and inverse invariants of mappings 510
List of special symbols 511
Author index 514
Subject index 520
|
| any_adam_object | 1 |
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| classification_rvk | SK 280 |
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| discipline | Mathematik |
| edition | Rev. and completed ed. |
| format | Book |
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| id | DE-604.BV006574765 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:48:33Z |
| institution | BVB |
| isbn | 3885380064 |
| language | English Polish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004194886 |
| oclc_num | 20464424 |
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| owner | DE-739 DE-20 |
| owner_facet | DE-739 DE-20 |
| physical | VIII, 529 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Heldermann |
| record_format | marc |
| series | Sigma series in pure mathematics |
| series2 | Sigma series in pure mathematics |
| spelling | Engelking, Ryszard ca. 20./21. Jh. Verfasser (DE-588)1244557080 aut General topology Ryszard Engelking Rev. and completed ed. Berlin Heldermann 1989 VIII, 529 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Sigma series in pure mathematics 6 Dimension Espace uniforme Exercice topologie Proximité Topologie générale Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Sigma series in pure mathematics 6 (DE-604)BV000012120 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004194886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Engelking, Ryszard ca. 20./21. Jh General topology Sigma series in pure mathematics Dimension Espace uniforme Exercice topologie Proximité Topologie générale Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | General topology |
| title_auth | General topology |
| title_exact_search | General topology |
| title_full | General topology Ryszard Engelking |
| title_fullStr | General topology Ryszard Engelking |
| title_full_unstemmed | General topology Ryszard Engelking |
| title_short | General topology |
| title_sort | general topology |
| topic | Dimension Espace uniforme Exercice topologie Proximité Topologie générale Topologie gtt Topologie ram Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Dimension Espace uniforme Exercice topologie Proximité Topologie générale Topologie Topology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004194886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012120 |
| work_keys_str_mv | AT engelkingryszard generaltopology |