Set theory and metric spaces / Irving Kaplansky.
Editor: New York : Chelsea, 1977Edición: 2nd edDescripción: xii, 140 p. : il. ; 24 cmISBN: 0828402981Tema(s): Set theory | Metric spacesOtra clasificación: 03Exx (54Exx 03-01 54-01)Preface xi 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] 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] 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 1. Examples of Metric Spaces [117] 2. Set Theory and Algebra [122] 3. The Transition to Topological Spaces [127] Selected Bibliography [133] Index [137]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 03 K17 (Browse shelf) | Available | A-5203 |
Includes index.
"Text differs only slightly form that of the 1st edition."
Bibliografía: p. 133-135.
Preface xi --
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] --
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] --
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 --
1. Examples of Metric Spaces [117] --
2. Set Theory and Algebra [122] --
3. The Transition to Topological Spaces [127] --
Selected Bibliography [133] --
Index [137] --
MR, 56 #5297
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