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

Frobenius theorem      351
Function      16
functor      242
Functorial properties of $h_{*}$       3 34
Fundamental group      371
Fundamental group of $P^{2}$       373
Fundamental group of $S^{l}$       345
Fundamental group of $S^{n}$       369
Fundamental group of $\mathbb{R}^{n}-0$       360
Fundamental group of a product      371
Fundamental group of deformation retract      361
Fundamental group of double torus      374 452
Fundamental group of dunce cap      444
Fundamental group of figure eight      362 373
Fundamental group of infinite earring      500
Fundamental group of linear graph      511
Fundamental group of m-fold projective plane      453
Fundamental group of n-fold torus      452
Fundamental group of theta space      362 432
Fundamental group of torus      371 442
Fundamental group of wedge of circles      434 436
Fundamental group of wedge of spaces      438
Fundamental group, when abelian      335
Fundamental group, when countable      499 500
Fundamental group, when finitely generated      500
Fundamental group, when uncountable      500
Fundamental theorem of algebra      354
G/H      146 331
G/H as topological group      146
G/H, regularity      146
General lifting lemma      478
General linear group      146
General nonseparation theorem      390
General position      308 310
General separation theorem      380 392
Generalized Continuum Hypothesis      62
Generated by elements      411 421.
Generated by subgroups      407 412
Generator of cyclic group      346
Geometrically independent      309
Graph of a function      171
Greater cardinality      62
Greatest lower bound      27
Greatest lower bound, property      27
Group of covering transformations      487
Groupoid properties      326
Hahn — Mazurkiewicz Theorem      275
Half-open interval      84
Ham sandwich theorem      359
Hausdorff condition      98
Hausdorff condition and closedness of diagonal      100
Hausdorff condition and convergent sequences      99
Hausdorff condition and perfect maps      199
Hausdorff condition and uniqueness of extensions      112 240
Hausdorff condition for box topology      116
Hausdorff condition for manifold      227
Hausdorff condition for metric space      129
Hausdorff condition for orbit space      199
Hausdorff condition for order topology      100
Hausdorff condition for product space      100 116 196
Hausdorff condition for quotient space      142
Hausdorff condition for subspace      100 196
Hausdorff condition for topological group      146
Hausdorff condition vs. $T_{1}$ axiom      99
Hausdorff condition vs. regularity      195 197
Hausdorff condition, normality      202
Hausdorff condition, paracompactness      257
Hausdorff condition, subspace      129
Hausdorff maximum principle      69
Hausdorff metric      281
Hausdorff space      98 (see also “Hausdorff condition”)
Have the same cardinality      51
Hilbert cube      128
Homeomorphism      105
Homeomorphism vs. continuous bijective map      106 167
Homogeneous space      146
Homology group      455
Homomorphism      330
Homomorphism, induced by a map      333 (see also ht)
Homomorphism, induced by a path      331 (see also a)
Homotopic maps      323
Homotopy      323
Homotopy as path in function space      288
Homotopy equivalence      363
Homotopy equivalence vs. deformation retraction      365 366
Homotopy equivalence, induces isomorphism of $\pi_{1}$       364
Homotopy extension lemma      381
Homotopy inverse      363
Homotopy type      363
Homotopy type of contractible space      366
Homotopy, effect on $h_{*}$       360 363 364
Homotopy, straight-line      325
Hypothesis      7
Identification space      139
Identity function      21
Image      16 19
Imbedding      105
Imbedding theorem for a compact manifold      226 314
Imbedding theorem for a completely regular space      217
Imbedding theorem for a linear graph      308
Imbedding theorem for a manifold      316
Imbedding theorem for a space of dimension m      311
Imbedding, isometric      133
Immediate predecessor      25
Immediate successor      25
inclusion      4
Index of a subgroup      514
Index set      36
Indexed family of sets      36
Indexing function      36
Indiscrete topology      77
Induction principle      32
Induction principle, strong      33
Induction principle, transfinite      67
Inductive definition      47 (see also “Recursive definition”)
Inductive dimension      315
Inductive set      32 67
Inf A      27
Infimum      27
Infinite broom      162
Infinite earring      436
Infinite earring, fundamental group      500
Infinite earring, no universal covering      487
Infinite sequence      38
Infinite series      135
Infinite set      44
Infinite set via injective and bijective functions      57
Initial point of a path      323
Initial point of an oriented line segment      447 506
Injective function      18
Int A      95
Integers      32
Interior point of a set      95
Interior point of an arc      379
Intermediate-value theorem      147 154
Intersection      6 12 36
interval      25 84
Intervals in $\mathbb{R}$ compactness      173
Intervals in $\mathbb{R}$ connectedness      154
Intervals in $\mathbb{R}$ topological dimension      305
Invariance of domain      383 385
Inverse function      18
Inverse image      19
Isolated point      176
Isometric imbedding      133
Isometric imbedding in complete metric space      269 271
Isometry      181
Isomorphism      105 330
J-tuple      113
Jordan curve theorem      390

Jordan separation theorem      379
K-fold covering      341
K-plane      310
K-topology on $\mathbb{R}$       82 (see also $\mathbb{R}_{K}$ )
Kernel of homomorphism      330
Klein bottle      454
Kuratowski 14-set problem      102
Kuratowski lemma      72
Labelling      447
Labelling scheme      449 (see also “Scheme”)
labels      447
Larger topology      77
largest element      27
Least normal subgroup      419
Least normal subgroup, generators      420
Least upper bound      27
Least upper bound property      27
Least upper bound property and compactness      172 177
Least upper bound property and local compactness      183
Least upper bound property for $\mathbb{R}$       31
Least upper bound property for well-ordered sets      66
Least upper bound property vs. greatest lower bound property      29
Lebesgue number      175
Lebesgue number lemma      175
Left coset      146 330
Left inverse      21
Length of a word      412
Lens space      494
Lifting      342
Lifting correspondence      345
Lifting lemma for path homotopies      343
Lifting lemma for paths      342
Lifting lemma, general      478
Limit of a sequence      100
Limit point      97
Limit point compactness      178
Limit point compactness vs. compactness      179
Limit point compactness vs. countable compactness      181
Limit point vs. $T_{1}$ axiom      99
Lindeloef condition      192 (see also “Regular Lindeloef space”)
Lindeloef condition for $\mathbb{R}^{2}_{l}$       193
Lindeloef condition for $\mathbb{R}_{l}$       192
Lindeloef condition for closed subspace      194
Lindeloef condition for products      193
Lindeloef condition for subspace      193
Lindeloef condition, effect of continuous function      194
Line with two origins      227
Linear continuum      31 153
Linear continuum, compact subspaces      172
Linear continuum, connected subspaces      153
Linear continuum, long line      158
Linear continuum, normality      206
Linear continuum, ordered square      155
Linear graph      308 394 502
Linear graph, fundamental group      511
Linear graph, imbedding in $\mathbb{R}^{3}$       308
Linear graph, local path connectedness      504
Linear graph, local simple connectedness      504
Linear graph, semilocal simple connectedness      504
Linear graph, topological dimension      308
Linear order      24
Little ell-two topology      128
Local compactness      182
Local compactness and least upper bound property      183
Local compactness and perfect maps      199
Local compactness for orbit space      199
Local compactness of $\mathbb{R}$ and $\mathbb{R}^{n}$ and $\mathbb{R}^{\omega}$       182
Local compactness of products      186
Local compactness of subspace      185
Local compactness, implies compactly generated      283
Local connectedness      161
Local connectedness of quotient space      163
Local connectedness vs. weak local connectedness      162
Local homeomorphism      338
Local metrizability      218 261
Local path connectedness      161
Local simple connectedness      495
Local simple connectedness vs. simple connectedness      499
Locally compact Hausdorff space, Baire condition      299
Locally compact Hausdorff space, complete regularity      213
Locally compact Hausdorff space, regularity      205
Locally discrete      254
Locally Euclidean      316
Locally finite collection      244
Locally finite family      112
Locally finite family vs. locally finite collection      245
Logical equivalence      8
Logical quantifiers      9
Long line      158 317
Long line, connectedness      159
Long line, path connectedness      159
Loop      331
Lower bound      27
Lower limit topology      82 (see also $\mathfrak{R}_{l}$ )
M-fold projective plane      452
M-fold projective plane, first homology group      456
M-fold projective plane, fundamental group      453
m-tuple      37
Manifold      225 316
Manifold, imbedding in $R^{n}$       226 314 316
Manifold, metrizability      227
Manifold, necessity of Hausdorff condition      227
Manifold, regularity      227
Manifold, topological dimension      314 316
Mapping      16
Maximal element      70
Maximal tree      509
Maximum principle      69
Maximum principle vs. well-ordering theorem      73
Maximum principle vs. Zorn’s lemma      70 72
Maximum value theorem of calculus      147
Maximum value theorem, general      174
Metric      119
Metric for $\mathbb{R}$       120
Metric for $\mathbb{R}^{n}$       122
Metric for $\mathbb{R}^{\omega}$       125
Metric for Discrete topology      120
Metric space      120
Metric topology      119
Metric, bounded      129
Metrically equivalent      270
Metrizability of $S_{\Omega}$ and $\bar{S_{\Omega}}$       181
Metrizability of $\mathbb{R}^{J}$       133
Metrizability of $\mathbb{R}^{n}$       123
Metrizability of $\mathbb{R}^{\omega}$       125 132
Metrizability of $\mathbb{R}_{l}$       194
Metrizability of compact Hausdorff space      218
Metrizability of manifolds      227
Metrizability of ordered square      194
Metrizability of products      133 134
Metrizability of regular Lindelof space      218
Metrizability of regular second-countable space      215
Metrizability of Stone- $\check{C}$ ech compactification      242
Metrizable space      120
Minimal uncountable well-ordered set      66 (see also “ $S_{\Omega}$ ”)
Moebius band      450
Monomorphism      330
N(f, a)      (see “Winding number”)
N-fold torus      451
N-fold torus, first homology group      456
N-fold torus, fundamental group      452
Nagata — Smimov metrization theorem      250
Negation      9
Neighborhood      96
Nested sequence of sets      170
Net      187
No-retraction theorem      348
Nonseparation theorem, arc in $S^{2}$       389
Nonseparation theorem, general      390
Nonseparation theorem, topologist’s sine curve in $S^{2}$       393

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