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

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Предметный указатель

Product space, local compactness      186
Product space, metrizability      131 132
Product space, normality      197 201 202 205
Product space, paracompactness      256 259
Product space, regularity      197
Product space, second-countability      191
Product space, subbasis      88 113
Products of continuous maps      112
Products of covering maps      336
Products of open maps      139
Products of quotient maps      138 141 187 289
Projection maps      88 113
Projective n-space      353
Projective plane      352 see
Proper map      285 315
Proper subset      4
Punctured euclidean space      155 see
Punctured plane      321 see
q      32
Quantifiers, logical      9
Quasicomponent      163
Quasicomponent vs. component      163 235
Quotient map      135
Quotient map, composites      138
Quotient map, products      138 141 187 289
Quotient operation in R      31
Quotient space      136
Quotient topology      136
Quotient topology vs. product topology      138 141 187
Quotient topology, Hausdorff condition      139 140 206
Quotient topology, normality      206
Quotient topology, subspace      138 '
R      30
R, compact sets in      174
R, connected sets in      154
R, metric for      118
R, paracompactness      255
R, standard topology      82
R, uncountability      176
Range of a function      16
Rational numbers      32
Ray in ordered set      86
Real numbers      30 see also “R”
Reciprocal      31
Recursion formula      48 55
Recursive definition      48
Recursive definition, principle      49 55
Recursive definition, transfinite      68
Refinement of a collection      225 251
Regular covering map      398
Regular Lindelof space, metrizability      220
Regular Lindelof space, normality      205
Regular Lindelof space, paracompactness      259
Regular space      195 see
Regularity      195
Regularity of G/H      145
Regularity of products      197
Regularity of subspaces      197
Regularity of topological groups      145
Regularity vs. complete regularity      238
Regularity vs. Hausdorff condition      195 200
Regularity vs. metrizability      217 249
Regularity vs. normality      195 200 201 205
Relation      21
Restriction of a function      16
Restriction of a relation      28
retract      216 345 see “Retraction”
Retraction      330
Retraction, $B^2\rightarrow S^1$       342
Retraction, $B^{n+1}\rightarrow S^n$       368 373
Retraction, onto logarithmic spiral      221
Retraction, onto knotted x-axis      221
Retraction, deformation      373
Retraction, strong deformation      345
Reverse of a path      320
Right inverse      21
Rule of assignment      15
Russell’s paradox      62
Saturated set      135
Schoenflies theorem      385
Schroeder — Bernstein theorem      52
Second category      294
Second coordinate of ordered pair      13
Second-countability      190
Second-countability of       190
Second-countability of $R^\omega$       190
Second-countability of compact metric space      194
Second-countability of connected locally compact metric space      261
Second-countability of products      191
Second-countability of subspaces      191
Second-countability vs. countable dense subset      191 194
Second-countability vs. Lindeloef condition      191 194
Second-countable space      190 see also “Second-countability”
Section of       40
Section of ordered set      66
Semilocally simply connected      393
Separable      192 see
Separation by continuous functions of closed sets      211
Separation by continuous functions of points from closed sets      220
Separation of a space      147
Separation theorems, by simple closed curve      377 386
Separation theorems, by $A\cup B$       377 386
Separation theorems, by simple closed curve      375 383
Separation theorems,       385
Sequence lemma      128
Sequences      37
Sequences in product spaces      116 281
Sequences vs. closure      128 190
Sequences vs. compactness      179 181
Sequences vs. continuity      128 190
Sequences, sums, differences, products and quotients      132
Sequential compactness      179
Sequential compactness vs. compactness      181 194
Set      3 4
Set, "Set of all sets" paradox      62
Set, rules for specifying      58
Shrinking lemma      224
Simple closed curves      375
Simple closed curves, generates $\pi_1$ of       387
Simple closed curves, separates       377 385
Simple closed curves, separates       375 383
Simple order      24
Simplicial 2-complex      306 see
Simply connected space      328
Simply connected space,       327
Simply connected space,       350
Simply connected space,       326
Simply connected space,       347 351
Simply connected space,       350
Simply connected space, contractible space      361
Slice in covering space      3 31
Slice in product space      168
Smaller topology      78
Smallest element of ordered set      27
Smirnov metrization theorem      260
Sorgenfrey plane      193 see
Space-filling curve      271
Special Van Kampen theorem      348
Sphere, unit      138 156 see “
Square metric      120 267 see
Square root of 2, irrationality      36
Square roots, existence      35
Star convex set      330
Stereographic projection      350 367
Stone — Cech compactification      241
Stone — Cech compactification of $S_\Omega$       243
Stone — Cech compactification of       243
Stone — Cech compactification, connectedness      243
Stone — Cech compactification, metrizability      243
Stone — Cech compactification, uniqueness      242

Stone’s theorem      256
Straight-line homotopy      321
Strict partial order      69
Strictly coarser topology      77
Strictly finer topology      77
Strong deformation retract      345
Strong deformation retract, fundamental group      345
Strong deformation retraction      345
Strong deformation retraction of onto $\theta$ and eight      345 346
Strong deformation retraction of onto $S^{n-1}$       345
Strong deformation retraction vs. homotopy equivalence      372
Stronger topology      78
Subbasis for a topology      82
Subnet      188
Subsequence      179
Subset      4
subspace      89
Subspace of metric space      126
Subspace vs. box topology      114
Subspace vs. order topology      90
Subspace vs. product topology      90 114
Subspace vs. quotient topology      138
Subspace, basis for      89
Subspace, compactness      165
Subspace, complete regularity      236
Subspace, connectedness      147
Subspace, countable dense subset      193
Subspace, first-countability      191
Subspace, Hausdorff condition      99 197
Subspace, Lindeloef condition      194 220
Subspace, normality      197 201.205
Subspace, paracompactness      256
Subspace, regularity      197
Subspace, second-countability      191
Subtraction operation      31
Sup metric      267
Sup metric vs. uniform metric      267
Sup metric, completeness      267 268
Superset      232
Support      222
surface      223
Surjective function      19
Theta space      346 373
Theta space, separates       386
Tietze extension theorem      212
Topological dimension      302
Topological dimension in a metric space      304
Topological dimension of a 2-complex      306
Topological dimension of a 2-manifold      306
Topological dimension of a linear graph      305
Topological dimension of a manifold      314 315
Topological dimension of a set in       305
Topological dimension of a set in       313 315
Topological dimension of a subspace      302
Topological dimension of a triangular region      306 359
Topological dimension of a union      304 315
Topological dimension of [a, b]      304
Topological group      144
Topological group, $\pi_1$ is abelian      331
Topological group, closedness of $A\cdot B$       173 188
Topological group, complete regularity      237
Topological group, covering spaces of      342 398
Topological group, Hausdorff condition      145
Topological group, normality      207
Topological group, paracompactness      260
Topological group, regularity      145
Topological imbedding      105
Topological property      104
Topological space      76
Topologically complete space      270 see
Topologist’s sine curve      158
topology      76
Topology, generated by a basis      78 80
Topology, generated by a subbasis      82
Torus      134 333
Torus equals doughnut surface      334
Torus, covering by $R\times R$       333
Torus, double      355
Torus, fundamental group      352
Torus, vector fields on      366
Totally bounded      275
Totally disconnected      152
Tower      74
Transcendental number      52
Transfinite induction      67
Transfinite recursive definition      68
Translation of       309
Triangle inequality      117
Trivial group      328
Trivial topology      77
Tube      168
Tube lemma      169
Tube lemma, generalized      172
Tychonoff theorem      232
Tychonoff theorem, countable      278
Tychonoff theorem, finite      167
Uncountability of $\mathscr{P} (Z_+)$       50
Uncountability of $\{0, 1\}^\omega$       50
Uncountability of R      176
Uncountability of transcendental numbers      52
Uncountable set      46
Uncountable well-ordered set      66 see
Uncountable well-ordered set, existence      73
Uniform boundedness principle      297
Uniform continuity theorem of calculus      146
Uniform continuity theorem, general      180
Uniform convergence      129
Uniform convergence on compact sets      282 see
Uniform convergence, Weierstrass M-test      134
Uniform limit theorem      130
Uniform limit theorem, converse fails      133
Uniform limit theorem, partial converse      172
Uniform metric      122 266 see
Uniform metric vs. sup metric      267
Uniform metric, completeness      266
Uniform structure      292
Uniform topology      122 266 see
Uniform topology vs. compact convergence topology      283
Uniform topology vs. pointwise convergence topology      283
Uniform topology vs. product topology      122
Uniform topology, compactness properties      181 277 279
Uniform topology, independence of metric      289
Uniformly bounded      278
union      5 12 38
Universal covering group      343
Universal covering space      341
Universal covering space, existence      397
Universal covering space, uniqueness      342 397
Universal extension property      216
Universal extension property vs. absolute retract      221
Universal neighborhood extension property      221
Upper bound      27
Urysohn lemma      207
Urysohn lemma for completely regular spaces      237
Urysohn lemma, strong form      215
Urysohn Metrization Theorem      217
Vacuously true      7
Value of a function      16
van Kampen theorem      349
Van Kampen theorem, special      348
Vanishing at infinity      279
Vector field      364
Vector field on       364
Vector field on       369
Vector field on       367
Vector field on       369 374
Vector field on Klein bottle      366
Vector field on torus      366
Vertices of a linear graph      304
Weaker topology      78

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