Set theory and metric spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Chelsea Publ. Co.
1977
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 140 S. graph. Darst. |
Staff View
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| 245 | 1 | 0 | |a Set theory and metric spaces |c Irving Kaplansky |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Chelsea Publ. Co. |c 1977 | |
| 300 | |a XII, 140 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Ensembles, Théorie des | |
| 650 | 4 | |a Espaces métriques | |
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| 650 | 7 | |a complétude |2 inriac | |
| 650 | 7 | |a espace métrique |2 inriac | |
| 650 | 7 | |a théorie ensemble |2 inriac | |
| 650 | 4 | |a Metric spaces | |
| 650 | 4 | |a Set theory | |
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Record in the Search Index
| _version_ | 1804116387160915968 |
|---|---|
| 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 |
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| author_role | aut |
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| author_variant | i k ik |
| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SK 150 |
| ctrlnum | (OCoLC)2964845 (DE-599)BVBBV001946217 |
| dewey-full | 511/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.3 |
| dewey-search | 511/.3 |
| dewey-sort | 3511 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| language | English |
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| spelling | Kaplansky, Irving 1917-2006 Verfasser (DE-588)119264358 aut Set theory and metric spaces Irving Kaplansky 2. ed. New York Chelsea Publ. Co. 1977 XII, 140 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie des Espaces métriques Espaces métriques ram axiome choix inriac complétude inriac espace métrique inriac théorie ensemble inriac Metric spaces Set theory Reihe (DE-588)4049197-3 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Reihe (DE-588)4049197-3 s Metrischer Raum (DE-588)4169745-5 s 1\p DE-604 Mengenlehre (DE-588)4074715-3 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001268639&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kaplansky, Irving 1917-2006 Set theory and metric spaces Ensembles, Théorie des Espaces métriques Espaces métriques ram axiome choix inriac complétude inriac espace métrique inriac théorie ensemble inriac Metric spaces Set theory 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 Irving Kaplansky |
| title_fullStr | Set theory and metric spaces Irving Kaplansky |
| title_full_unstemmed | Set theory and metric spaces Irving Kaplansky |
| title_short | Set theory and metric spaces |
| title_sort | set theory and metric spaces |
| topic | Ensembles, Théorie des Espaces métriques Espaces métriques ram axiome choix inriac complétude inriac espace métrique inriac théorie ensemble inriac Metric spaces Set theory Reihe (DE-588)4049197-3 gnd Metrischer Raum (DE-588)4169745-5 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Ensembles, Théorie des Espaces métriques axiome choix complétude espace métrique théorie ensemble Metric spaces Set theory Reihe Metrischer Raum Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001268639&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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