Munkres J. — Topology :: Электронная библиотека попечительского совета мехмата МГУ

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Munkres J. — Topology

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Название: Topology

Автор: Munkres J.

Аннотация:

This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

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Рубрика: Математика/Геометрия и топология/Общая топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-e издание

Год издания: 2000

Количество страниц: 276

Добавлена в каталог: 20.04.2005

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Предметный указатель

Complete regularity (cont.) of $S_{\Omega}\times\bar{S_{\Omega}}$       212
Complete regularity (cont.) of $\mathbb{R}^{2}_{l}$       212
Complete regularity (cont.) of subspace      211
Complete regularity (cont.) of topological group      213
Complete regularity (cont.) vs. normality      211 212
Complete regularity (cont.) vs. regularity      214
Complete regularity of $\mathbb{R}^{J}$ in box topology      213
Complete regularity of locally compact Hausdorff space      213
Complete regularity of product space      211
Complete set of relations      425
Completely normal space      205
Completely regular space      211 (see also “Complete regularity”)
Completeness and Baire condition      296
Completeness of $Y^{J}$ in uniform metric      267
Completeness of $Y^{x}$ in compact-open topology      289
Completeness of $\mathbb{R}^{J}$ in uniform metric      267
Completeness of $\mathbb{R}^{n}$       265
Completeness of $\mathbb{R}^{\omega}$       265
Completeness of $\mathcal{C}(X, Y)$ in sup metric      268
Completeness of $\mathcal{C}(X, Y)$ in uniform metric      267
Completeness of $\mathcal{I}^{2}$       271
Completeness of $\mathfrak{B}(X, Y)$ in uniform metric      267
Completeness of closed subspace      264
Completeness vs. compactness      276
Completion      269
Completion, uniqueness      271
Component      159
Component of $\mathbb{R}^{\omega}$ in box topology      162
Component of $\mathbb{R}^{\omega}$ in uniform topology      162
Component vs. path component      161
Component vs. quasicomponent      163 236
Composite of continuous functions      107
Composite of covering maps      341 485 487
Composite of functions      17
Composite of quotient maps      141
Conclusion      7
Cone      499
Conjugacy class      481
Conjugate elements      419
Conjugate subgroups      481
Connected component      159
Connected space      148 (see also “Connectedness”)
Connected sum of projective planes      452
Connected sum of tori      451
Connectedness      148
Connectedness in a linear continuum      153
Connectedness in box topology      151
Connectedness in finite complement topology      152
Connectedness of $\mathbb{R}^{\omega}$       151
Connectedness of $\mathbb{R}_{K}$       177
Connectedness of a product space      152
Connectedness of closure      150
Connectedness of continuous image      150
Connectedness of finite products      150
Connectedness of long line      159
Connectedness of ordered square      156
Connectedness of subspace      148
Connectedness of topologist’s sine curve      156
Connectedness vs. path connectedness      156
Constant path      327
CONTAINS      4
Continuity and change of range      108
Continuity and closedness of graph      171
Continuity at a point      104
Continuity in variables separately      112
Continuity of algebraic operations in $\mathbb{R}$       131 135
Continuity of composites      107
Continuity of constant function      107
Continuity of inclusion      107
Continuity of maps from quotient spaces      142
Continuity of maps into products      110 117
Continuity of metric      126
Continuity of min(f, g)      112
Continuity of products of maps      112
Continuity of restriction      108
Continuity of uniform limit      132
Continuity via nets      188
Continuity via sequences      130 190
Continuity, $\epsilon-\delta$ formulation      129
Continuity, basis criterion      103
Continuity, closed set criterion      104
Continuity, closure criterion      104
Continuity, local formulation      108
Continuity, subbasis criterion      103
Continuous function      102 (see also “Continuity”)
Continuous image of a compact space      166
Continuous image of a connected space      150
Continuous image of a Lindeloef space      194
Continuous image of a space with a countable dense subset      194
Continuum Hypothesis      62 205
Contractible space      330
Contractible space, homotopy type      366
Contraction      182 270
Contraction and fixed points      182
Contraction vs. shrinking map      182
Contrapositive      8
Convergent net      187
Convergent sequence      98
Convergent sequence in a product space      118 265
Convergent sequence in compact convergence topology      283
Convergent sequence in Hausdorff space      99
Convergent sequence in point-open topology      282
Convergent sequences in compact convergence topology      283
Convergent sequences in point-open topology      282
Converges uniformly      131
CONVERSE      9
Convex set in $\mathbb{R}^{n}$       325
Convex set in an ordered set      90 153
Coordinate function      110
Coordinate of $\omega$ -tuple      38
Coordinate of J-tuple      113
Coordinate of m-tuple      37
Coset      146 330
Countability      45
Countability of $\mathbb{Z}$       44
Countability of $\mathbb{Z}_{+}\times\mathbb{Z}_{+}$       45 48
Countability of algebraic numbers      51
Countability of countable unions      48
Countability of finite products      49
Countability of rationals      48
Countability of subsets      48
Countability via injective and surjective maps      45
Countable basis      190 (see also “Second-countability”)
Countable basis at a point      130 190
Countable compactness      181
Countable dense subset      192
Countable dense subset in $\mathbb{R}^{I}$       195
Countable dense subset in $\mathbb{R}^{J}$       195
Countable dense subset in $\mathbb{R}_{l}$       192
Countable dense subset in subspace      194
Countable dense subset, effect of continuous function      194
Countable intersection property      235
Countable set      45 (see also “Countability”)
Countably infinite      44
Countably locally discrete      252
Countably locally finite      245
Counterclockwise loop      404
Counterimage      19
Covering      164
Covering dimension      305
Covering map      336
Covering map is local homeomorphism      338
Covering map is open      336
Covering map, composite      341 487
Covering map, restrictions      338 484
Covering of subspace      164
Covering space      336
Covering space of $P^{2}$       372
Covering space of $S^{I}$       337 338 482
Covering space of $\mathbb{R}^{2}-0$       340

Covering space of figure eight      340 374 375 492 493
Covering space of linear graph      505
Covering space of torus      339 483
Covering space, classification      482
Covering space, equivalence      478
Covering space, existence      495
Covering space, k-fold      341
Covering space, regular      489
Covering space, topological properties      341 500
Covering space, universal      484
Covering transformation      487
Cube in $\mathbb{R}^{n}$       314
Curve      225
Curve, simple closed      379
Curved triangle      471
Cutting a region apart      458
CW complex      445
Cyclic group      346
D(x, A)      175
Decomposition space      139
Deformation retract      361
Deformation retract, fundamental group of      361
Deformation retraction      361
Deformation retraction vs. homotopy equivalence      365 366
Degree of a map      367
DeMorgan’s laws      11
Dense subset      191
Diagonal      101
Diameter of a set      121
dictionary order      26
Difference of two sets      10
Dimension, topological      305 (see also “Topological dimension”)
Direct sum      408 409
Direct sum, existence      409
Direct sum, extension condition      408 410
Direct sum, uniqueness      410
Directed set      187 188
Discrete topology      77
Disjoint sets      6
Distance      119
Distance from x to A      175
Distributive laws for $\bigcup$ and $\bigcap$       11
Domain      16
Double torus      374 452
Double torus, fundamental group      374
Doubly punctured plane      362
Dunce cap      443
Dunce cap, fundamental group      444
Edge of a linear graph      308 394 502
Edge of a polygonal region      447
Edge of curved triangle      471
Edge path      506
Edge path, reduced      507
Element of a set      4
Elementary divisors      424
Elementary operations on schemes      460
Empty interior      295
Empty set      6
End points of arc      308 378
Epimorphism      330
Epimorphism, $\epsilon$ -ball      119
Epimorphism, $\epsilon$ -neighborhood of a set      177
Equality symbol      4
Equicontinuity      276
Equicontinuity vs. compactness      278 279
Equicontinuity vs. total boundedness      277
Equivalence class      22
Equivalence of compactifications      237
Equivalence of covering maps      478
Equivalence of covering maps, existence      480 482
Equivalence of labelling schemes      461
Equivalence relation      22
Euclidean metric      122 128
Euclidean space      38
Euler number      506 514 515
Evaluation map      271 286
Evenly covered      336
Eventually zero      51
Expansion Lemma      260
Extension condition for direct sums      408 410
Extension condition for free abelian groups      411
Extension condition for free groups      421
Extension condition for free products      414 418 419
External direct sum      409
External free product      415
Extreme Value Theorem      174
F*g      326
Family of sets      36
Fibonacci numbers      56
Field      31
Figure-eight space      340 362
Figure-eight space, covering space      340 374 375 492 493
Figure-eight space, fundamental group      373
Final point of oriented line segment      447 506
Final point of path      323
Fine topology      289
Fine topology is Baire      300
Finer topology      77
Finer topology, basis criterion      81
Finite axiom of choice      61
Finite complement topology      77
Finite complement topology, compactness      166
Finite complement topology, connectedness      152
Finite dimensional      305
Finite intersection property      169
Finite presentation      425
Finite set      39
Finitely generated group      421
Finitely presented group      425
Finitely presented group as fundamental group      445
Finiteness of cartesian products      43
Finiteness of subsets      43
Finiteness of unions      43
Finiteness vs. injective and suijective maps      43
First category set      295
First coordinate      13
First homology group      455
First homology group of m-fold projective plane      456
First homology group of n-fold torus      456
First homotopy group      (see “Fundamental group”)
First-countability      131 190
First-countability of $\mathbb{R}_{l}$       192
First-countability of metric space      131
First-countability of product      191
First-countability of subspace      191
First-countability, implies compactly generated      283
First-countable space      (see “First-countability”)
Fixed point      158 182
Fixed point theorem for $B^{2}$       351
Fixed point theorem for $B^{n}$       353
Fixed point theorem for a contraction      182 270
Fixed point theorem for a shrinking map      182
Fixed point theorem for retract of $B^{2}$       353
Fixed point theorem for [0, 1]      158
Fixed-point-free action      493
Free Abelian group      411
Free abelian group, extension condition      411
Free abelian group, rank      411
Free abelian group, subgroup is free abelian      412
Free generators for a group      421
Free group      421
Free group on a set      422
Free group, extension condition      421
Free group, subgroup is free      514
Free homotopy of loops      403
Free product      413
Free product, existence      415
Free product, extension condition      414 418 419
Free product, external      415
Free product, uniqueness      418

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