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.

Язык:

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

Sorgenfrey plane      193 (see also “ $\mathbb{R}^{2}$ ”)
Sphere, unit      139 156 “
Square metric      122 (see also “ $\rho$ ”)
Standard bounded metric      121
Standard topology, on $\mathbb{R}$       81
Standard topology, on $\mathbb{R}^{2}$       87
Star-convex set      334
Stereographic projection      369
Stone- $\check{C}$ ech compactification      241
Stone- $\check{C}$ ech compactification of $S_{\Omega}$       242
Stone- $\check{C}$ ech compactification of $\mathbb{Z}_{+}$       242
Stone- $\check{C}$ ech compactification, existence      239
Stone- $\check{C}$ ech compactification, extension condition      240
Stone- $\check{C}$ ech compactification, metrizability      242
Stone- $\check{C}$ ech compactification, uniqueness      240
Straight-line homotopy      325
Strict partial order      68
Strictly coarser topology      77
Strictly finer topology      77
Strong continuity      137
Strong induction principle      33
Stronger topology      78
Subbasis      82
Subbasis for order topology      86
Subbasis for product topology      88 114
Subgraph      503
Subgroup of free abelian group      412
Subgroup of free group      514
Subnet      188
Subsequence      179
Subset      4
Subspace topology      88
Subspace topology in metric space      129
Subspace topology vs. box topology      116
Subspace topology vs. order topology      91
Subspace topology vs. product topology      89 116
Subspace topology, basis      89
Subspace topology, compactness      164
Subspace topology, complete regularity      211
Subspace topology, connectedness      148
Subspace topology, countable dense subset      194
Subspace topology, first-countability      191
Subspace topology, Hausdorff condition      100 196
Subspace topology, Lindeloef condition      193 194
Subspace topology, local compactness      185
Subspace topology, normality      203 205
Subspace topology, paracompactness      254
Subspace topology, regularity      196
Subspace topology, second-countability      191
Subspace topology, topological dimension      306
Sum of groups      407
Sup A      27
Sup metric      268
Sup metric vs. uniform metric      268
Superset      233
Support      225 257
Supremum      27
surface      225 370
Surface with boundary      476
Surface, classification      457
Surjective function      18
Symmetric neighborhood      146
System of free generators      421
Theta space      362 394
Theta space, fundamental group      432
Theta space, separates $S^{2}$       395
Tietze extension theorem      219
Topological completeness      270 (see also “Complete metric space”)
Topological dimension      305
Topological dimension of 1 -manifold      308
Topological dimension of 2-manifold      308 352
Topological dimension of a union      307 308
Topological dimension of closed subspace      306
Topological dimension of closed subspace of $\mathbb{R}^{N}$       316
Topological dimension of compact manifold      314
Topological dimension of compact subspace of $\mathbb{R}$       305
Topological dimension of compact subspace of $\mathbb{R}^{2}$       306
Topological dimension of compact subspace of $\mathbb{R}^{N}$       313
Topological dimension of linear graph      308
Topological dimension of manifold      316
Topological dimension of triangular region      352
Topological dimension of [0, 1]      305
Topological group      145
Topological group, $\pi_{1}$ is abelian      335
Topological group, closedness of $A\cdotB$       172 188
Topological group, complete regularity      213
Topological group, covering space of      483
Topological group, Hausdorff condition      146
Topological group, normality      207
Topological group, paracompactness      261
Topological group, regularity      146
Topological group, second-countability      195
Topological imbedding      105
Topological property      105
Topological space      76
Topologist's sine curve      157
Topologist's sine curve, components      160
Topologist’s sine curve (cont.), connectedness      156
Topologist’s sine curve (cont.), does not separate $S^{2}$       393
Topologist’s sine curve (cont.), path components      160
Topologist’s sine curve (cont.), path connectedness      157
topology      76
Topology, generated by a basis      78 80
Topology, generated by a subbasis      82
Torsion subgroup      412 424
Torus      339

Torus as quotient space      136 140
Torus, equals doughnut surface      339
Torus, fundamental group      371 442
Torus-type scheme      463
Totally bounded      275
Totally bounded vs. equicontinuity      277
Totally disconnected      152
Tower      73
Transcendental number      51
Transfinite induction      67
Translation of $\mathbb{R}^{N}$       310
TREE      507
Tree, fundamental group      508
Tree, maximal      509
Triangle inequality      119
Triangulable      471
Triangulation      471
Trivial homomorphism      335
Trivial topology      77
Tube      167
Tube lemma      168
Tube lemma, generalized      171
Tukey lemma      72
Tychonoff theorem      234
Tychonoff theorem for countable products      280
Tychonoff theorem for finite products      167
Tychonoff theorem via well-ordering theorem      236
Uncountability of $(0,1)^{\omega}$       49
Uncountability of $\mathbb{R}$       177
Uncountability of $\mathfrak{P}(\mathbb{Z}_{+})$       50
Uncountability of transcendental numbers      51
Uncountable set      45
Uncountable well-ordered set      74 (see also “ $S_{\Omega}$ ”)
Uniform boundedness principle      299
Uniform continuity theorem      147 176
Uniform convergence      131
Uniform convergence on compact sets      283
Uniform convergence, Weierstrass M-test for      135
Uniform limit theorem      132
Uniform limit theorem, converse fails      134
Uniform limit theorem, partial converse      171
Uniform metric      124 266
Uniform metric vs. sup metric      268
Uniform metric, completeness      267
Uniform structure      292
Uniform topology      124 266
Uniform topology vs. box topology      124
Uniform topology vs. compact convergence topology      285
Uniformly continuous      176
union      5 12 36
Unit ball      135 331 “
Unit circle      106 (see also “ $S^{1}$ ”)
Unit sphere      156 (see also “ $S^{n}$ ”)
Universal covering space      484
Universal covering space, existence      498
Universal extension property      223
Upper bound      27 70
Urysohn lemma      207
Urysohn lemma, strong form      213
Urysohn Metrization Theorem      215
Utilities graph      308 394
Utilities graph, nonembeddability      396
Vacuously true      7
Value of a function      16
Vanish at infinity      280
Vanish precisely on A      213
Vector field      350
Vertex of a curved triangle      471
Vertex of a linear graph      308 394 502
Vertex of a polygonal region      447
Weak local connectedness      162
Weak local connectedness vs. connectedness      162
Weaker topology      78
Wedge of circles      434 435
Wedge of circles, existence      437
Wedge of circles, fundamental group      434 436
Wedge of spaces      438
Weierstrass M-test      135
Well-ordered set      63
Well-ordered set, $\mathbb{Z}_{+}$       32
Well-ordered set, $\mathbb{Z}_{+}\times\mathbb{Z}_{+}$       63
Well-ordered set, compact subspaces      172
Well-ordered set, dictionary order      64
Well-ordered set, finite      64
Well-ordered set, normality      202
Well-ordered set, subsets well-ordered      63
Well-ordered set, uncountable      66
Well-ordering theorem      65
Well-ordering theorem and axiom of choice      67 73
Well-ordering theorem and maximum principle      70 73
Well-ordering theorem, applied      236 246
Winding number      398 403
Winding number as an integral      405
Winding number of simple closed curve      404 406
Word      412 415
Word, reduced      413
Zermelo      65
Zorn’s Lemma      70
Zorn’s lemma vs. maximum principle      75
Zorn’s lemma, applied      72 233 236 509
[f]      324
[G, G]      422
[x, y]      330
“If... then,” meaning of      7
“Onto” function      18
“Or,” meaning of      5

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