Munkres J.R. — Topology: A First Course :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

Identity function      20
Image      16 17
Image set      15 16
Imbedding      105 see
Imbedding theorem for a 2-complex      310
Imbedding theorem for a compact manifold      223 314
Imbedding theorem for a completely regular space      237
Imbedding theorem for a linear graph      308
Imbedding theorem for a manifold      315
Imbedding theorem for an m-dimensional space      310 315
Imbedding theorem into       220
Immediate predecessor      25
Immediate successor      25
Index set      37
Indexed family of sets      37
Indexing function      37
Indiscrete topology      77
Induced homomorphism      see “ $h_*$

”
Induction, Principle of      32
Induction, principle of, transfinite      67
Inductive definition      see “Recursive definition”
Inductive set in a well-ordered set      67
Inductive set in R      32
Inessential map      357
Inessential map, induces zero homomorphism      358 371
Infinite broom      164
Infinite sequence      37
Infinite series      133
Infinite set      45 57
Initial point of a path      319
Injective function      19
Int A      95
Integers      32
Interior of a set      94
Intermediate value theorem of calculus      146
Intermediate value theorem, general      154
Intersection      6 12 38
Intersects      95
interval      25 84
Intervals in R, compactness      174
Intervals in R, connectedness      154
Intervals in R, topological dimension      304
Inverse function      19
Inverse image      17
Irrationality of $\sqrt{2}$       36
Irrationals, $G_\delta$ set      250
Irrationals, Baire      296
Irrationals, topologically complete      270
Isometric imbedding      132
Isometric imbedding into a complete space      268 271
Isometric imbedding surjectivity      182
Isometry      182
Isomorphism      105
J-tuple      38
Jordan curve theorem      383
Jordan separation theorem      375
K-fold covering      336
K-plane      309
Kuratowski 14-set problem      101
Larger topology      78
Largest element of an ordered set      27
Laws of algebra      33
Laws of exponents      35
Laws of inequalities      34
Least upper bound      27
Least upper bound property      27
Least upper bound property for R      31
Least upper bound property for well-ordered sets      67
Least upper bound property vs. greatest lower bound property      29
Lebesgue dimension      302
Lebesgue number      179
Lebesgue number lemma      179
Left inverse      21
Lens space      357
Lifting lemma for path homotopies      338
Lifting lemma for paths      337
Lifting lemma, general      342 390
Lifting of a map      336
Limit point      96
Limit point compact space      178
Limit point compactness of products      182
Limit point compactness vs. compactness      178 181 194
Limit point compactness vs. countable compactness      182
Lindelof condition      191 see
Lindelof condition for       192
Lindelof condition for       193
Lindelof condition for $S_\Omega$ and $\widehat{S_\Omega}$       194
Lindelof condition for products      193 195 235
Lindelof condition for subspaces      194 220
Lindelof condition vs. second-countability      191 194
Lindelof space      191
Linear continuum      31 152
Linear continuum, compact sets in      173
Linear continuum, connected sets in      152
Linear graph      304
Linear graph, imbedding in       308
Linear graph, topological dimension      305
Linear order      24
lnvariance of domain      378 387
Local compactness      182 see
Local compactness of and $R^{\omega}$       183
Local compactness of products      186
Local compactness, implies compactly generated      282
Local connectedness      161
Local connectedness of and $R^{\omega}$       161
Local connectedness vs. connectedness in kleinen      163
Local connectedness vs. local path connectedness      162
Local homeomorphism      334
Local metrizability      220
Local metrizability vs. metrizability      220 260
Local path connectedness      161
Local simple connectedness      393 398
Locally compact Hausdorff space is Baire      296
Locally compact Hausdorff space, complete regularity      237
Locally compact Hausdorff space, imbedding in       315
Locally compact Hausdorff space, one-point compactification      183
Locally compact Hausdorff space, regularity      205
Locally compact Hausdorff space, second-countability      261
Locally discrete collection      254
Locally finite collection      245
Locally finite indexed family      111 224
Locally finite indexed family vs. locally finite collection      246
Logical equivalence      8
Logical quantifiers      9
Long line      159
Long line, paracompactness      259
Loop      326
Lower bound      27
Lower limit topology      82 see
lub A      27
m-tuple      36
Manifold      223
Manifold, Hausdorff condition is needed      225
Manifold, imbeds in       223
Manifold, imbeds in $R^{2m+1}$       314 315
Manifold, metrizability      224
Manifold, topological dimension      306 314 315
Mapping      16
Maximum principle      69
Maximum principle, applied      232 235
Maximum principle, intuitive proof      70
Maximum principle, proof      74
Maximum value theorem of calculus      146
Maximum value theorem, general      175
Mean convergence topology      284
Metric      117
Metric space      119
Metric space       121
Metric space , uniform metric      266
Metric space R      118

Metric space, , uniform metric      122
Metric space, $\ell^2$       126
Metric space, Hausdorff condition      126
Metric space, normality      198
Metric space, paracompactness      256
Metric space, subspace      126
Metrizability of $I\times I$ in dictionary order      195
Metrizability of       131
Metrizability of       121
Metrizability of $R^{\omega}$       123
Metrizability of $R^{\omega}$ in box topology      130
Metrizability of $R_l}      195
Metrizability of $S_{\Omega}$       179
Metrizability of $\overline{S_{\Omega}}$       131
Metrizability of manifolds      224
Metrizability of products      126 132
Metrizability of R      118
Metrizable space      119
Minimal uncountable well-ordered set      66 see
Multiplication operation      30
Nagata — Smirnov condition      245
Nagata — Smirnov metrization theorem, necessity      253
Nagata — Smirnov metrization theorem, sufficiency      249
Negation      9
Negative number      31
Neighborhood      96
Neighborhood retract      221
Nested sequence of sets      171
Net      187
Nonseparation theorems      378 382
Norm      120 ' '
Normal space      195 see
Normality      195
Normality of       202
Normality of adjunction space      221
Normality of closed subspace      205
Normality of coherent topology      216
Normality of compact Hausdorff space      198
Normality of metric space      198
Normality of paracompact space      255
Normality of product      197 201 202 205
Normality of regular Lindeloef space      205
Normality of subspace      197 201 205
Normality of well-ordered set      200
Normality vs. complete regularity      236
Normality vs. regularity      195 201 202 205
Nowhere-differentiable function      297
Number of elements in a set      40
Number of elements in a set, uniqueness      43
Odd integer      35
One      31
One-point compactification      183
One-to-one function      19
Open covering      164
Open interval      25 84
Open map      91 135
Open ray      86
Open refinement      251
Open set      76
Open set, relative to subspace      89
Operation, binary      30
Orbit space      357
Orbit space, fundamental group      357 see
Order of a collection      302
Order relation      24
Order topology      85 see
Order topology vs. subspace topology      90
Order topology, compact sets in      173 177
Order topology, Hausdorff condition      99
Order topology, normality      200
Order topology, regularity      205
Order topology, subbasis      91
Order type      25
Order-preserving function      25
Ordered field      31
Ordered pair      13
Paracompact space      225 255
Paracompact-manifold      261
Paracompactness      255
Paracompactness and partitions of unity      225
Paracompactness of       256 259
Paracompactness of $S_\Omega$       259 261
Paracompactness of compact Hausdorff space      255
Paracompactness of long line      259
Paracompactness of product      256 259
Paracompactness of R      255
Paracompactness of regular Lindeloef space      259
Paracompactness of subspace      256
Paracompactness vs. metrizability      256 260
Paracompactness vs. normality      255
Partial order      71
Partial order, axioms      72 187
Partial order, strict      69
Partition of a set      23
Partition of unity      222 225
Pasting lemma      108
Path      155
Path component      160
Path component vs. component      162
Path connectedness      155
Path connectedness of       155
Path connectedness of $I\times I$ in dictionary order      156
Path connectedness of       155 350
Path connectedness of       156
Path connectedness of deleted comb space      157
Path connectedness of long line      159
Path connectedness of topologist’s sine curve      158
Path connectedness vs. connectedness      156 158
Path homotopy      319
Path-homotopy class      320
Path-induced homomorphism      327
Peano curve      271
Peano space      274
Piecewise linear function      299
Plane in       309
Point of accumulation      96
Point-finite collection      247
Point-finite indexed family      224
Point-open topology      280
Point-open topology vs. compact convergence topology      283 290
Point-open topology vs. compact-open topology      286
Point-open topology, convergent sequences in      281
Pointwise bounded collection      278
Pointwise convergence topology      280 see
Positive integers      32
Positive number      31
Power set      11
Preimage      17
Principle of Induction      32
Principle of recursive definition      49 55
Principle of transfinite induction      67
Principle of transfinite recursive definition      68 '
Product space      86 113
Product space equals point-open topology      280
Product space vs. box topology      114
Product space vs. quotient topology      138 141 187 289
Product space vs. subspace topology      90 114
Product space vs. uniform topology, on       122
Product space, basis for      87 114
Product space, closures in      100 116
Product space, compactness      167 232 278
Product space, complete regularity      236
Product space, connectedness      150
Product space, convergent sequences in      116 281
Product space, countable dense subset      195
Product space, first-countability      191
Product space, fundamental group of      351
Product space, Hausdorff condition      99 115 197
Product space, limit point compactness      182
Product space, Lindeloef condition      193 195 235

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