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Munkres J.R. — Topology: A First Course
Munkres J.R. — Topology: A First Course



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Название: Topology: A First Course

Автор: Munkres J.R.

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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 413

Добавлена в каталог: 08.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"If ... then"      7
$(h_{x_0})_*$      329 see
$a^n$, definition      35 55
$B(x, \epsilon)$      117
$B^2$      133 see
$B^n$      155
$B^n$, compactness      175
$B^n$, path connectedness      155
$B^n$, simple connectedness      327
$e_\chi$ (constant path)      322
$F_\sigma$ set      250
$G_\delta$ set      194 248
$G_\delta$ set and strong Urysohn lemma      215
$G_\delta$ set is Baire      296
$G_\delta$ set is topologically complete      270
$G_\delta$ set, $f^{-1} (c)$ is a      215 238
$G_\delta$ set, closed set is a      248 250
$G_\delta$ set, irrationals      250
$G_\delta$ set, points of continuity form a      296 297
$G_\delta$ set, rationals      295
$h_*$, dependence on base point      330
$h_*$, dependence on homotopy class of h      369
$h_*$, functorial properties      329
$I\times I$ in dictionary order, closures in      101
$I\times I$ in dictionary order, connectedness      156
$I\times I$ in dictionary order, linear continuum      154
$I\times I$ in dictionary order, local connectedness      163
$I\times I$ in dictionary order, metrizability      195
$I\times I$ in dictionary order, path connectedness      156
$I^I$, countable dense subset      195
$l_2$      126
$l_2$, completeness      270
$l_2$, countable dense subset      195
$n\textrm{th}$ root function, continuity      111
$n\textrm{th}$ root function, existence      158
$P^2$      352
$P^2$, fundamental group      353
$P^2$, surface      352
$R^2 - 0$      321
$R^2 - 0$, covering by $R\times R$      334
$R^2 - 0$, fundamental group      343
$R^2$, standard topology      87
$R^J$ in box topology is Baire      297
$R^J$ in box topology is topological group      144
$R^J$ in product topology is Baire      297
$R^J$ in product topology is topological group      144
$R^J$ in product topologyá metrizability      131
$R^J$ in product topologyá normality      205
$R^J$ in uniform topology      122
$R^J$ in uniform topology is Baire      297
$R^J$ in uniform topology is topological group      144
$R^J$ in uniform topologyá completeness      266
$R^n - 0$      155
$R^n - 0$, fundamental group      344
$R^n - 0$, path connectedness      155 350
$R^n$      37
$R^n$, basis for      115
$R^n$, compact sets in      174
$R^n$, completeness      264
$R^n$, local compactness      183
$R^n$, local path connectedness      161
$R^n$, metrics for      121
$R^n$, second-countability      190
$R^n$, simple connectedness      326
$R^\infty$      116 125 274
$R^\omega$      37
$R^\omega$ in box topology      see also “$R^J$ in box topology”
$R^\omega$ in box topology, complete regularity      237
$R^\omega$ in box topology, components      163
$R^\omega$ in box topology, connectedness      152
$R^\omega$ in box topology, metrizability      130
$R^\omega$ in box topology, normality      206
$R^\omega$ in box topology, paracompactness      206
$R^\omega$ in product topology      see also “$R^J$ in product topology”
$R^\omega$ in product topology, completeness      265
$R^\omega$ in product topology, local compactness      183
$R^\omega$ in product topology, local path connectedness      161
$R^\omega$ in product topology, metrizability      123
$R^\omega$ in product topology, second-countability      190
$R^\omega$ in uniform topology      see also “$R^J$ in uniform topology”
$R^\omega$ in uniform topology, components      163
$R^\omega$ in uniform topology, second-countability      191
$R_+, \overline{R}_+$      31
$R_l$      82
$R_l$ vs. standard topology on R      82
$R_l$, countability axioms      192
$R_l$, metrizability      195
$R_l$, normality      202
$R_l$, paracompactness      256 259
$R_l^2$      193
$R_l^2$, complete regularity      237
$R_l^2$, Lindelof condition      193
$R_l^2$, normality      202
$R_l^2$, paracompactness      256
$S^1$      106
$S^1$, covering by R      332
$S^1$, covering spaces classified      393
$S^1$, coverings by $S^1$      335 336
$S^1$, fundamental group      340
$S^2$      138
$S^2$, simple connectedness      347 351
$S^2$, vector fields on      367
$S^n$      156
$S^n$, compactness      175
$S^n$, fixed-point theorem for      374
$S^n$, path connectedness      156
$S^n$, simple connectedness      350
$S^n$, vector fields on      369 374
$S_\Omega \times \overline{S}_\Omega$, complete regularity      236
$S_\Omega \times \overline{S}_\Omega$, normality      201
$S_\Omega \times \overline{S}_\Omega$, paracompactness      256
$S_\Omega$      66
$S_\Omega$, compactness properties      178
$S_\Omega$, countability axioms      194
$S_\Omega$, metrizability      179
$S_\Omega$, paracompactness      259 261
$S_\Omega$, Stone — Cech compactification      243
$S_\Omega$, uniqueness      73
$T_1$ axiom      99
$U(A, \epsilon)$      177
$X^J$      38
$X^m$      36
$X^\omega$      37
$Z_+$      32
$\beta(x)$      see “Stone — Cech compactification”
$\epsilon$-ball      117
$\epsilon$-neighborhood of a set      177
$\hat{\alpha}$      327
$\hat{\alpha}$ is isomorphism      327
$\hat{\alpha}$, independence of path      330
$\mathscr{C}(X, Y)$      267 see “Compact-open “Uniform
$\mathscr{C}(X, Y)$, closedness in $Y^X$      267 281 283
$\mathscr{C}(X, Y)$, compact subsets of      290
$\mathscr{C}(X, Y)$, completeness      267
$\mathscr{P}(A)$      11
$\mathscr{T}_f$      77
$\mathscr{T}_f$, $T_1$ axiom      100
$\mathscr{T}_f$, compactness      167
$\mathscr{T}_f$, connectedness      151
$\omega$-tuple      37
$\overline{d}$      119
$\overline{S}_\Omega$      66
$\overline{S}_\Omega$, metrizability      131
$\overline{\rho}$      122 266 see
$\pi_1 (X, x_0)$      326 see
$\rho$      120 267 see
$\sigma$-locally discrete      254
$\sigma$-locally finite      247
2-complex      306
2-complex, imbedding in $R^5$      310
2-complex, topological dimension      306
2-sphere      138 see
Abelian fundamental group      330 354 355
Absolute neighborhood retract      221
Absolute retract vs. universal extension properly      221
Accumulation point of a net      188
Action of a group on a space      356
Addition operation      30
Adjunction space      221
Alexander horned sphere      385
Algebraic numbers      51
ANR      221
Antipodal map      353
Antipodal point      352
Antipode-preserving map      361
ar      221
ARC      375
Archimedean ordering      33
Arzela’s theorem      279 292
Ascoli’s theorem, classical version      277
Ascoli’s theorem, general version      290
Axiom of Choice      59
Axiom of choice, equivalent statements      62 74
Axiom of choice, finite      61
Baire category theorem      294
Baire category theorem, special case      177 203
Baire space      293
Baire space, $G_\delta$ set      296
Baire space, $R^J$      297
Baire space, compact Hausdorff space      294
Baire space, complete metric space      294
Baire space, fine topology on $\mathscr{C}(X, Y)$      297
Baire space, irrationals      296
Baire space, locally compact Hausdorff space      296
Baire space, open subset      296
Ball, unit      see “$B^n$”
Barber of Seville paradox      48
Base point      326
Base-point choice, effect on $h_*$      330
Base-point choice, effect on $\pi_1$      328
Basis for a topology      78 81
Bd A      101
Bijective function      19
Binary operation      30
Bing metrization theorem      254
Bolzano — Weierstrass property      178
Borsuk theorem      377
Borsuk — Ulam theorem for $S^2$      361
Boundary      101
Bounded above      27
Bounded below      27
Bounded metric, standard      119
Bounded set      119
Box topology      113
Box topology vs. product topology      114
Box topology, basis for      114
Box topology, compactness properties      181
Box topology, Hausdorff condition      115
Box topology, subspace      114
Brouwer fixed-point theorem for $B^2$      365
Brouwer fixed-point theorem for $B^n$      369
Brouwer invariance of domain      378 387
Cantor set      177
Cardinality, comparability for two sets      68
Cardinality, greater      62
Cardinality, same      52
Cartesian product of two sets      13
Cartesian product, general      36—38
Cauchy sequence      264
Choice axiom      see “Axiom of choice”
Choice function      59
Circle, unit      see “$S^1$”
Cl A      95
Classification of covering spaces      388 392 393
Closed graph      172
Closed interval      84
Closed map      135 172
Closed ray      86
Closed refinement      251
Closed set      92
Closed set in subspace      94
Closure      94
Closure in a subspace      95
Closure of a cartesian product      100 116
Closure of a connected set      149
Closure of a union      100 246
Closure via basis elements      95
Closure via limit points      97
Closure via nets      188
Closure via sequences      128 190
Cluster point      96
Coarser topology      77
Cofinal      187
Coherent topology      216
Collection      11
Comb space      156
Compact convergence topology      282 see
Compact convergence topology vs. compact-open topology      286
Compact convergence topology vs. pointwise convergence topology      283 290
Compact convergence topology vs. uniform topology      283
Compact convergence topology, convergent sequences in      282
Compact convergence topology, first-countability      283
Compact convergence topology, independence of metric      287
Compact convergence topology, regularity      283
Compact Hausdorff space is Baire      294
Compact Hausdorff space, $G_5$ set is Baire      296
Compact Hausdorff space, components      235
Compact Hausdorff space, imbedding in      237
Compact Hausdorff space, metrizability      220
Compact Hausdorff space, normality      198
Compact Hausdorff space, paracompactness      255
Compact Hausdorff space, quasicomponents      235
Compact space      164 see
Compact support      284
Compact-open topology      286 290
Compact-open topology vs. compact convergence topology      286
Compact-open topology, continuity of evaluation map      287
Compact-open topology, Hausdorff condition      289
Compact-open topology, regularity      289
Compactification      238 see
Compactification of (0, 1)      239
Compactification, induced by an imbedding      239
Compactification, one-point      183
Compactly generated space      282
Compactness      164 see
Compactness in $R^n$      174
Compactness in $\mathscr{C}(X, R^n)$      277 279
Compactness in $\mathscr{C}(X, Y)$      290
Compactness in $\mathscr{T}_f$      167
Compactness in Hausdorff metric      279
Compactness in order topology      173 177
Compactness in R      174
Compactness in uniform topology      181
Compactness of box topology      181
Compactness of closed intervals      174
Compactness of continuous image      167
Compactness of countable products      278
Compactness of finite products      167
Compactness of products      232
Compactness of subspace      165
Compactness via nets      188
Compactness via sequences      181
Compactness vs. completeness      275
Compactness vs. limit point compactness      178 181 194
Compactness vs. second-countability      194
Compactness, closed set criterion for      170
Comparability of cardinalities      68
Comparability of well-ordered sets      73
Complement      10
Complete graph on five vertices      304 386
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