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

Norm      122
Normal space      195 (see also “Normality”)
Normal subgroup      330
Normality      195
Normality of $\mathbb{R}^{J}$       203
Normality of $\mathbb{R}_{l}$       198
Normality of adjunction space      224
Normality of closed subspace      205
Normality of coherent topology      224
Normality of compact Hausdorff space      202
Normality of linear continuum      206
Normality of linear graph      502
Normality of metric space      202
Normality of orbit space      199
Normality of paracompact Hausdorff space      253
Normality of product      198 203
Normality of quotient space      199 443
Normality of regular Lindeloff space      205
Normality of regular second-countable space      200
Normality of subspace      203
Normality of topological group      207
Normality of well-ordered set      202
Normality vs. complete regularity      211 212
Normality vs. regularity      195 198 203
normalizer      487
Nowhere-differentiable function      300
Nulhomotopic map      323
Nulhomotopic map, induces trivial homomorphism      364
Nulhomotopy lemma      377
One-point compactification      185
One-point compactification, uniqueness      183
One-to-one correspondence      18
Open covering      164
Open interval      25 84
Open map      92 137
Open ray      86
Open refinement      245
Open set      76
Open set, relative to subspace      89
Operation on schemes      460
Operation, binary      30
Orbit      490
Orbit space      199 490
Order of a covering      305
Order of a group      346
Order of a group element      412
Order relation      24
Order topology      84
Order topology vs. subspace topology      91
Order topology, compact subspaces      172
Order topology, Hausdorff condition      100
Order topology, normality      202 206
Order topology, subbasis      86
Order type      25
Ordered field      31
Ordered pair      13
Ordered square      90
Ordered square is linear continuum      155
Ordered square, connectedness      156
Ordered square, metrizability      194
Ordered square, path connectedness      156
Oriented edge of a graph      506
Oriented line segment      447
Paracompact space      253 (see also “Paracompactness”)
Paracompactness      253
Paracompactness and perfect maps      260
Paracompactness of $S_{\Omega}$       260 261
Paracompactness of $\mathbb{R}^{J}$       257
Paracompactness of $\mathbb{R}^{n}$       253
Paracompactness of $\mathbb{R}^{\infty}$ in box topology      260
Paracompactness of $\mathbb{R}^{\omega}$       257
Paracompactness of closed subspace      254
Paracompactness of compact Hausdorff space      252
Paracompactness of metric space      257
Paracompactness of regular Lindelof space      257
Paracompactness of topological groups      261
Paracompactness vs. normality      253
Partial order      71
Partial order, axioms      87
Partial order, strict      68
Partition of a set      23
Partition of unity      225 258
Partition of unity, existence      225 259
Pasting edges together      448
Pasting lemma      108
Pasting regions together      458
Path      155
Path component      160
Path component vs. component      161
Path connectedness      155
Path connectedness of $B^{n}$       156
Path connectedness of $S^{n}$       156
Path connectedness of $\mathbb{R}^{n}-0$       156
Path connectedness of long line      159
Path connectedness of ordered square      156
Path connectedness of topologist’s sine curve      157
Path connectedness vs. connectedness      156
Path homotopy      323
Path, corresponding to edge path      506
Path-homotopy class      324
Path-induced homomorphism      331
Peano curve      271
Peano space      275
Perfect map      172 199
Perfect map and compactness      172
Perfect map and paracompactness      260
Perfectly normal space      213
Piecewise linear function      302
Plane in $\mathbb{R}^{N}$       310
Point-finite collection      248
Point-finite family      227
Point-open topology      281
Point-open topology vs. compact convergence topology      285
Point-open topology vs. compact-open topology      285
Point-open topology, equals product topology      282
Pointwise bounded      278
Pointwise convergence topology      281 (see also “Point-open topology”)
Polygonal region      447
Positive integers      32
Positive linear map of intervals in R      328
Positive linear map of oriented line segments      447
Power set      12
Precise refinement      258
Preimage      19
Presentation of a group      425
Principle of Induction      32
Principle of induction, transfinite      67
Principle of recursive definition      47 54
Principle of recursive definition, general      72
Product of continuous maps      112
Product of covering maps      339
Product of open maps      141
Product of path-homotopy classes      326
Product of paths      326
Product of quotient maps      141 143 145 186 289
Product space      114 (see also “Product topology”)
Product topology      86 114
Product topology vs. box topology      115
Product topology vs. point-open topology      282
Product topology vs. quotient topology      141 143. 186 289
Product topology vs. subspace topology      89 116
Product topology vs. uniform topology      124
Product topology, basis      86 115 116
Product topology, closures in      101 116
Product topology, compactness      167 234
Product topology, complete regularity      211
Product topology, connectedness      150 152
Product topology, convergent sequences      118 265
Product topology, first-countability      191
Product topology, Hausdorff condition      100 116 196

Product topology, Lindeloef condition      193
Product topology, local compactness      186
Product topology, metrizability      133 134
Product topology, normality      198 203
Product topology, paracompactness      257
Product topology, regularity      196
Product topology, second-countability      191
Product topology, subbasis      88 114
Products of covering map      339
Projection map      87 114
Projection map is open map      92
Projective n-space      373
Projective plane      372 (see also “ $P^{2}$ ”)
Projective-type scheme      463
Proper inclusion      4
Proper labelling scheme      463
Proper subset      4
Properly discontinuous      490
Pruefer manifold      317
Punctured euclidean space      156 (see also “ $\mathbb{R}^{2}-0$ ”)
Punctured plane      325 (see also “ $\mathbb{R}^{2}-0$ ”)
Quantifiers, logical      9
Quasicomponent      163
Quasicomponent vs. component      163 236
Quotient group      331
Quotient map      137
Quotient map, composites      141
Quotient map, products      141 143 145 186 289
Quotient map, restrictions      137 138 140
Quotient space      139 (see also “Quotient topology”)
Quotient topology      138
Quotient topology and continuous functions      142
Quotient topology, $T_{1}$ condition      141
Quotient topology, Hausdorff condition      142 199
Quotient topology, local compactness      199
Quotient topology, local connectedness      163
Quotient topology, normality      199
Quotient topology, regularity      199
Quotient topology, second-countability      199
Quotient topology, vs. product topology      141 143 145 186 289
Range of a function      16
Rank of a free abelian group      411
Rational number      32
Ray in ordered set      85
Recursive definition, principle      47 54
Recursive definition, principle, general principle      72
Reduced edge path      507
Reduced word      413
refinement      245 305
Regular covering space      489
Regular covering space is orbit space      491
Regular Lindeloef space metrizability      218
Regular Lindeloef space normality      205
Regular Lindeloef space paracompactness      257
Regular space      195 (see also “Regularity”)
Regularity      195
Regularity and perfect maps      199
Regularity of G/H      146
Regularity of locally compact Hausdorff space      205
Regularity of manifold      227
Regularity of orbit space      199
Regularity of products      196
Regularity of subspaces      196
Regularity of topological groups      146
Regularity vs. complete regularity      214
Regularity vs. Hausdorff condition      195 197
Regularity vs. metrizability      215
Regularity vs. normality      195 198 203
Relation      21
Relation on a free group      424
Relation on a free group complete set      425
Represented by a word      412
Restriction of a covering map      338 484
Restriction of a function      17
Restriction of a quotient map      137 138 140
Restriction of a relation      28
retract      223 348
Retraction      335 348
Retraction as quotient map      144
Reverse of a path      327
Right coset      330
Right inverse      21
Rule of assignment      15
Russell’s paradox      62
Saturated set      137
Scheme      449
Scheme, projective type      463
Scheme, proper      463
Scheme, torus type      463
Schoenflies theorem      392
Schroeder — Bemstein theorem      52
Second category set      295
Second coordinate of ordered pair      13
Second-countability      190
Second-countability and perfect maps      199
Second-countability of $\mathbb{R}$ and $\mathbb{R}^{n}$ and $\mathbb{R}^{\omega}$       190
Second-countability of $\mathbb{R}^{\omega}$ in uniform topology      190
Second-countability of $\mathbb{R}_{l}$       192
Second-countability of $\mathcal{C}(I, R)$       194
Second-countability of compact metric space      194
Second-countability of orbit space      199
Second-countability of products      191
Second-countability of subspace      191
Second-countability of topological group      195
Second-countability vs. countable dense subset      194
Second-countability vs. Lindeleof condition      194
Second-countable space      190 (see also “Second-countability”)
Section of a well-ordered set      66
Section of the positive integers      32
Seifert-van Kampen theorem      426
Seifert-van Kampen theorem, classical version      431
Seifert-van Kampen theorem, special case      369
Semilocally simply connected      494
Separable      192 (see also “Countable dense subset”)
Separates a space      378
Separates a space, into n components      378
Separates points from closed sets      218
Separation      148
Separation by continuous functions      211
Separation theorem, closed topologist’s sine curve in $S^{2}$       393
Separation theorem, general      380 392
Separation theorem, simple closed curve in $S^{2}$       379 390
Separation theorem, theta space in $S^{2}$       395
Sequence lemma      130
Sequences      38
Sequences and closure      130 190
Sequences and continuity      130 190
Sequential compactness      179
Sequential compactness vs. compactness      179
Shrinking lemma      227
Shrinking lemma, general      258
Shrinking map      182
Shrinking map and fixed points      182
Shrinking map vs. contraction      182
Simple closed curve      379
Simple closed curve, generates $\pi_{1}$ of $\mathbb{R}^{2} — 0$       401
Simple closed curve, separates $S^{2}$       379 390
Simple closed curve, winding number      404 406
Simple loop      404
Simple order      24
Simply connected      333
Simply connected vs. locally simply connected      499
Simply connected, $S^{n}$       369
Simply connected, star-convex set      334
Simply connected, tree      508
Slice in covering space      336
Slice in product space      167
Smaller topology      77
Smallest element of ordered set      27
Smirnov metrization theorem      261

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