Set theory and metric spaces
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| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Boston
Allyn & Bacon
1977
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Allyn and Bacon series in advanced mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1819733893160370176 |
|---|---|
| adam_text | Contents
Preface xi
1
Basic Set Theory 1
1.1 Inclusion 1
1.2 Operations on Sets 4
1.3 Partially Ordered Sets and Lattices 9
1.4 Functions 14
1.5 Relations; Cartesian Products 19
vii
viii contents
2
Cardinal Numbers 21
2.1 Countable Sets 21
2.2 Cardinal Numbers 27
2.3 Comparison of Cardinal Numbers; Zorn s Lemma 31
2.4 Cardinal Addition 40
2.5 Cardinal Multiplication 41
2.6 Cardinal Exponentiation 44
3
Well ordering; The Axiom of Choice 49
3.1 Well ordered Sets 49
3.2 Ordinal Numbers 55
3.3 The Axiom of Choice 58
3.4 The Continuum Problem 64
4
Basic Properties of Metric Spaces 67
4.1 Definitions and Examples 67
4.2 Open Sets 71
4.3 Convergence; Closed Sets 75
4.4 Continuity 80
CONTENTS ix
5
Completeness, Separability, and Compactness 84
5.1 Completeness 84
5.2 Separability 94
5.3 Compactness 98
6
Additional Topics 106
6.1 Product Spaces 106
6.2 A Fixed point Theorem 108
6.3 Category 111
Appendixes 115
7. Examples of Metric Spaces 117
2. Set Theory and Algebra 122
3. The Transition to Topological Spaces 127
Selected Bibliography 133
Index 137
|
| any_adam_object | 1 |
| author | Kaplansky, Irving 1917-2006 |
| author_GND | (DE-588)119264358 |
| author_facet | Kaplansky, Irving 1917-2006 |
| author_role | aut |
| author_sort | Kaplansky, Irving 1917-2006 |
| author_variant | i k ik |
| building | Verbundindex |
| bvnumber | BV008492742 |
| classification_rvk | SK 110 |
| ctrlnum | (OCoLC)633219174 (DE-599)BVBBV008492742 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV008492742 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T12:46:04Z |
| institution | BVB |
| isbn | 0828402981 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005585781 |
| oclc_num | 633219174 |
| open_access_boolean | |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XII,140 S.m.Abb. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Allyn & Bacon |
| record_format | marc |
| series2 | Allyn and Bacon series in advanced mathematics. |
| spellingShingle | Kaplansky, Irving 1917-2006 Set theory and metric spaces Reihe (DE-588)4049197-3 gnd Metrischer Raum (DE-588)4169745-5 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4049197-3 (DE-588)4169745-5 (DE-588)4074715-3 |
| title | Set theory and metric spaces |
| title_auth | Set theory and metric spaces |
| title_exact_search | Set theory and metric spaces |
| title_full | Set theory and metric spaces |
| title_fullStr | Set theory and metric spaces |
| title_full_unstemmed | Set theory and metric spaces |
| title_short | Set theory and metric spaces |
| title_sort | set theory and metric spaces |
| topic | Reihe (DE-588)4049197-3 gnd Metrischer Raum (DE-588)4169745-5 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Reihe Metrischer Raum Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005585781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kaplanskyirving settheoryandmetricspaces |