Topology.

Por: Dugundji, JamesSeries Allyn and Bacon series in advanced mathematicsEditor: Boston : Allyn and Bacon, 1966Descripción: xvi, 447 p. ; 24 cmTema(s): TopologyOtra clasificación: 54-01
Contenidos:
 Contents
I. Elementary Set Theory I
1 Sets [1]
2 Boolean Algebra [3]
3 Cartesian Product [7]
4 Families of Sets [8]
5 Power Set [10]
6 Functions, or Maps [10]
7 Binary Relations; Equivalence Relations [14]
8 Axiomatics [17]
9 General Cartesian Products [21]
Problems [25]
Ordinals and Cardinals [29]
1 Orderings [29]
2 Zorn’s Lemma; Zermelo’s Theorem [31]
3 Ordinals [36]
4 Comparability of Ordinals [38]
5 Transfinite Induction and Construction [40]
6 Ordinal Numbers [41]
7 Cardinals [45]
8 Cardinal Arithmetic [49]
9 The Ordinal Number Ω [54]
Problems [57]
III. Topological Spaces [62]
1 Topological Spaces [62]
2 Basis for a Given Topology [64]
3 Topologizing of Sets [65]
4 Elementary Concepts [68]
5 Topologizing with Preassigned Elementary Operations [72]
6 G6i Fai and Borel Sets [74]
7 Relativization [77]
8 Continuous Maps [78]
9 Piecewise Definition of Maps [81]
10 Continuous Maps into E1 [83]
11 Open Maps and Closed Maps [86]
12 Homeomorphism [87]
Problems [90]
IV. Cartesian Products [98]
1 Cartesian Product Topology [98]
2 Continuity of Maps [101]
3 Slices in Cartesian Products [103]
4 Peano Curves [104]
Problems [105]
V. Connectedness [107]
1 Connectedness [107]
2 Applications [110]
3 Components [111]
4 Local Connectedness [113]
5 Path-Connectedness [114]
Problems [116]
VI. Identification Topology; Weak Topology [120]
1 Identification Topology [120]
2 Subspaces [122]
3 General Theorems [123]
4 Spaces with Equivalence Relations [125]
5 Cones and Suspensions [126]
6 Attaching of Spaces [127]
7 The Relation K(f) for Continuous Maps [129]
8 Weak Topologies [131]
Problems [133]
VII. Separation Axioms [137]
1 Hausdorff Spaces [137]
2 Regular Spaces [141]
3 Normal Spaces [144]
4 Urysohn’s Characterization of Normality [146]
5 Tietze’s Characterization of Normality [149]
6 Covering Characterization of Normality [152]
7 Completely Regular Spaces [153]
Problems [156]
VIII. Covering Axioms [160]
1 Coverings of Spaces [160]
2 Paracompact Spaces [162]
3 Types of Refinements [167]
4 Partitions of Unity [169]
5 Complexes; Nerves of Coverings [171]
6 Second-countable Spaces; Lindelöf Spaces [173]
7 Separability [175]
Problems [177]
IX. Metric Spaces [181]
1 Metrics on Sets [181]
2 Topology Induced by a Metric [182]
3 Equivalent Metrics [184]
4 Continuity of the Distance [184]
5 Properties of Metric Topologies [185]
6 Maps of Metric Spaces into Affine Spaces [187]
7 Cartesian Products of Metric Spaces [189]
8 The Space l2(A); Hilbert Cube [191]
9 Metrization of Topological Spaces [193]
10 Gauge Spaces [198]
11 Uniform Spaces [200]
Problems [204]
X. Convergence [209]
1 Sequences and Nets [209]
2 Filterbases in Spaces [211]
3 Convergence Properties of Filterbases [213]
4 Closure in Terms of Filterbases [215]
5 Continuity; Convergence in Cartesian Products [215]
6 Adequacy of Sequences [217]
7 Maximal Filterbases [218]
Problems [220]
XI. Compactness [222]
1 Compact Spaces [222]
2 Special Properties of Compact Spaces [226]
3 Countable Compactness [228]
4 Compactness in Metric Spaces [233]
5 Perfect Maps [235]
6 Local Compactness [237]
7 σ-Compact Spaces [240]
8 Compactification [242]
9 k-Spaces [247]
10 Baire Spaces; Category [249]
Problems [251]
XII. Function Spaces [257]
1 The Compact-open Topology [257]
2 Continuity of Composition; the Evaluation Map [259]
3 Cartesian Products [260]
4 Application to Identification Topologies [262]
5 Basis for ZY [263]
6 Compact Subsets of ZY [265]
7 Sequential Convergence in the ^-Topology [267]
8 Metric Topologies; Relation to the c-Topology [269]
9 Pointwise Convergence [272]
10 Comparison of Topologies in ZY [274]
Problems [275]
XIII. The Spaces C(Y) [278]
1 Continuity of the Algebraic Operations [278]
2 Algebras in Ĉ(Y; c) [219]
3 Stone-Weierstrass Theorem [281]
4 The Metric Space C(Y) [284]
5 Embedding of Y in C( Y) [285]
6 The Ring Ĉ(Y) [287]
Problems [290]
XIV. Complete Spaces [292]
1 Cauchy Sequences [292]
2 Complete Metrics and Complete Spaces [293]
3 Cauchy Filterbases; Total Boundedness [296]
4 Baire’s Theorem for Complete Metric Spaces [299]
5 Extension of Uniformly Continuous Maps [302]
6 Completion of a Metric Space [304]
7 Fixed-Point Theorem for Complete Spaces [305]
8 Complete Subspaces of Complete Spaces [307]
9 Complete Gauge Structures [309]
Problems [312]
XV. Homotopy [315]
1 Homotopy [315]
2 Homotopy Classes [317]
3 Homotopy and Function Spaces [319]
4 Relative Homotopy [321]
5 Retracts and Extendability [322]
6 Deformation Retraction and Homotopy [323]
7 Homotopy and Extendability [326]
8 Applications [330]
Problems [332]
XVI. Maps into Spheres [335]
1 Degree of a Map Sn -> Sn [335]
2 Brouwer’s Theorem [340]
3 Further Applications of the Degree of a Map [341]
4 Maps of Spheres into Sn [343]
5 Maps of Spaces into Sn [346]
6 Borsuk’s Antipodal Theorem [347]
7 Degree and Homotopy [350]
Problems [353]
XVII. Topology of En [355]
1 Components of Compact Sets in En+1 [356]
2 Borsuk’s Separation Theorem [357]
3 Domain Invariance [358]
4 Deformations of Subsets of En+1 [359]
5 The Jordan Curve Theorem [361]
Problems [363]
XVIII. Homotopy Type [365]
1 Homotopy Type [365]
2 Homotopy-Type Invariants [367]
3 Homotopy of Pairs [368]
4 Mapping Cylinder [368]
5 Properties of X in C(f) [371]
6 Change of Bases in C(f) [372]
Problems [374]
XIX. Path Spaces; H-Spaces [376]
1 Path Spaces [376]
2 H- Structures [379]
3 H-Homomorphisms [381]
4 H-Spaces [383]
5 Units [384]
6 Inversion [386]
7 Associativity [387]
8 Path Spaces on H-Spaces [388]
Problems [390]
XX. Fiber Spaces [392]
1 Fiber Spaces [392]
2 Fiber Spaces for the Class of All Spaces [395]
3 The Uniformization Theorem of Hurewicz [399]
4 Locally Trivial Fiber Structures [404]
Problems [408]
Appendix One: Vector Spaces; Polytopes [410]
Appendix Two: Direct and Inverse Limits [420]
Index [437]
    Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Copy number Status Date due Barcode Course reserves
Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 54 D868 (Browse shelf) Available A-2251

TOPOLOGÍA

Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 54 D868 (Browse shelf) Ej. 2 Available A-9480
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
54 C748 Introduzione alla topologia / 54 C958 Fondements de la topologie générale / 54 C958i Foundations of general topology / 54 D868 Topology. 54 D868 Topology. 54 En57 General topology / 54 F272 Espace et dimension /

Contents --
I. Elementary Set Theory I --
1 Sets [1] --
2 Boolean Algebra [3] --
3 Cartesian Product [7] --
4 Families of Sets [8] --
5 Power Set [10] --
6 Functions, or Maps [10] --
7 Binary Relations; Equivalence Relations [14] --
8 Axiomatics [17] --
9 General Cartesian Products [21] --
Problems [25] --
Ordinals and Cardinals [29] --
1 Orderings [29] --
2 Zorn’s Lemma; Zermelo’s Theorem [31] --
3 Ordinals [36] --
4 Comparability of Ordinals [38] --
5 Transfinite Induction and Construction [40] --
6 Ordinal Numbers [41] --
7 Cardinals [45] --
8 Cardinal Arithmetic [49] --
9 The Ordinal Number Ω [54] --
Problems [57] --
III. Topological Spaces [62] --
1 Topological Spaces [62] --
2 Basis for a Given Topology [64] --
3 Topologizing of Sets [65] --
4 Elementary Concepts [68] --
5 Topologizing with Preassigned Elementary Operations [72] --
6 G6i Fai and Borel Sets [74] --
7 Relativization [77] --
8 Continuous Maps [78] --
9 Piecewise Definition of Maps [81] --
10 Continuous Maps into E1 [83] --
11 Open Maps and Closed Maps [86] --
12 Homeomorphism [87] --
Problems [90] --
IV. Cartesian Products [98] --
1 Cartesian Product Topology [98] --
2 Continuity of Maps [101] --
3 Slices in Cartesian Products [103] --
4 Peano Curves [104] --
Problems [105] --
V. Connectedness [107] --
1 Connectedness [107] --
2 Applications [110] --
3 Components [111] --
4 Local Connectedness [113] --
5 Path-Connectedness [114] --
Problems [116] --
VI. Identification Topology; Weak Topology [120] --
1 Identification Topology [120] --
2 Subspaces [122] --
3 General Theorems [123] --
4 Spaces with Equivalence Relations [125] --
5 Cones and Suspensions [126] --
6 Attaching of Spaces [127] --
7 The Relation K(f) for Continuous Maps [129] --
8 Weak Topologies [131] --
Problems [133] --
VII. Separation Axioms [137] --
1 Hausdorff Spaces [137] --
2 Regular Spaces [141] --
3 Normal Spaces [144] --
4 Urysohn’s Characterization of Normality [146] --
5 Tietze’s Characterization of Normality [149] --
6 Covering Characterization of Normality [152] --
7 Completely Regular Spaces [153] --
Problems [156] --
VIII. Covering Axioms [160] --
1 Coverings of Spaces [160] --
2 Paracompact Spaces [162] --
3 Types of Refinements [167] --
4 Partitions of Unity [169] --
5 Complexes; Nerves of Coverings [171] --
6 Second-countable Spaces; Lindelöf Spaces [173] --
7 Separability [175] --
Problems [177] --
IX. Metric Spaces [181] --
1 Metrics on Sets [181] --
2 Topology Induced by a Metric [182] --
3 Equivalent Metrics [184] --
4 Continuity of the Distance [184] --
5 Properties of Metric Topologies [185] --
6 Maps of Metric Spaces into Affine Spaces [187] --
7 Cartesian Products of Metric Spaces [189] --
8 The Space l2(A); Hilbert Cube [191] --
9 Metrization of Topological Spaces [193] --
10 Gauge Spaces [198] --
11 Uniform Spaces [200] --
Problems [204] --
X. Convergence [209] --
1 Sequences and Nets [209] --
2 Filterbases in Spaces [211] --
3 Convergence Properties of Filterbases [213] --
4 Closure in Terms of Filterbases [215] --
5 Continuity; Convergence in Cartesian Products [215] --
6 Adequacy of Sequences [217] --
7 Maximal Filterbases [218] --
Problems [220] --
XI. Compactness [222] --
1 Compact Spaces [222] --
2 Special Properties of Compact Spaces [226] --
3 Countable Compactness [228] --
4 Compactness in Metric Spaces [233] --
5 Perfect Maps [235] --
6 Local Compactness [237] --
7 σ-Compact Spaces [240] --
8 Compactification [242] --
9 k-Spaces [247] --
10 Baire Spaces; Category [249] --
Problems [251] --
XII. Function Spaces [257] --
1 The Compact-open Topology [257] --
2 Continuity of Composition; the Evaluation Map [259] --
3 Cartesian Products [260] --
4 Application to Identification Topologies [262] --
5 Basis for ZY [263] --
6 Compact Subsets of ZY [265] --
7 Sequential Convergence in the ^-Topology [267] --
8 Metric Topologies; Relation to the c-Topology [269] --
9 Pointwise Convergence [272] --
10 Comparison of Topologies in ZY [274] --
Problems [275] --
XIII. The Spaces C(Y) [278] --
1 Continuity of the Algebraic Operations [278] --
2 Algebras in Ĉ(Y; c) [219] --
3 Stone-Weierstrass Theorem [281] --
4 The Metric Space C(Y) [284] --
5 Embedding of Y in C( Y) [285] --
6 The Ring Ĉ(Y) [287] --
Problems [290] --
XIV. Complete Spaces [292] --
1 Cauchy Sequences [292] --
2 Complete Metrics and Complete Spaces [293] --
3 Cauchy Filterbases; Total Boundedness [296] --
4 Baire’s Theorem for Complete Metric Spaces [299] --
5 Extension of Uniformly Continuous Maps [302] --
6 Completion of a Metric Space [304] --
7 Fixed-Point Theorem for Complete Spaces [305] --
8 Complete Subspaces of Complete Spaces [307] --
9 Complete Gauge Structures [309] --
Problems [312] --
XV. Homotopy [315] --
1 Homotopy [315] --
2 Homotopy Classes [317] --
3 Homotopy and Function Spaces [319] --
4 Relative Homotopy [321] --
5 Retracts and Extendability [322] --
6 Deformation Retraction and Homotopy [323] --
7 Homotopy and Extendability [326] --
8 Applications [330] --
Problems [332] --
XVI. Maps into Spheres [335] --
1 Degree of a Map Sn -> Sn [335] --
2 Brouwer’s Theorem [340] --
3 Further Applications of the Degree of a Map [341] --
4 Maps of Spheres into Sn [343] --
5 Maps of Spaces into Sn [346] --
6 Borsuk’s Antipodal Theorem [347] --
7 Degree and Homotopy [350] --
Problems [353] --
XVII. Topology of En [355] --
1 Components of Compact Sets in En+1 [356] --
2 Borsuk’s Separation Theorem [357] --
3 Domain Invariance [358] --
4 Deformations of Subsets of En+1 [359] --
5 The Jordan Curve Theorem [361] --
Problems [363] --
XVIII. Homotopy Type [365] --
1 Homotopy Type [365] --
2 Homotopy-Type Invariants [367] --
3 Homotopy of Pairs [368] --
4 Mapping Cylinder [368] --
5 Properties of X in C(f) [371] --
6 Change of Bases in C(f) [372] --
Problems [374] --
XIX. Path Spaces; H-Spaces [376] --
1 Path Spaces [376] --
2 H- Structures [379] --
3 H-Homomorphisms [381] --
4 H-Spaces [383] --
5 Units [384] --
6 Inversion [386] --
7 Associativity [387] --
8 Path Spaces on H-Spaces [388] --
Problems [390] --
XX. Fiber Spaces [392] --
1 Fiber Spaces [392] --
2 Fiber Spaces for the Class of All Spaces [395] --
3 The Uniformization Theorem of Hurewicz [399] --
4 Locally Trivial Fiber Structures [404] --
Problems [408] --
Appendix One: Vector Spaces; Polytopes [410] --
Appendix Two: Direct and Inverse Limits [420] --
Index [437] --

MR, 57 #17581

There are no comments on this title.

to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a biblioteca.antonio.monteiro@gmail.com

Powered by Koha