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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
Complete graph on four vertices      386
Complete metric space      264
Complete regularity of $R^\omega$ in box topology      237
Complete regularity of $R_1^2$      237
Complete regularity of locally compact Hausdorff space      237
Complete regularity of products      236
Complete regularity of subspace      236
Complete regularity of topological group      237
Complete regularity vs. normality      236
Complete regularity vs. regularity      238
Completely normal space      206
Completely regular space      211 236 see
Completeness of $G_\delta$ set      270
Completeness of $R^n$      264
Completeness of $R^\omega$      265
Completeness of $\ell^2$      270
Completeness of $\mathscr{C}(X, Y)$ in uniform metric      267
Completeness of closed subspace      264
Completeness of irrationals      270
Completeness of open subspace      270
Completeness of products      270
Completeness of sup metric      267
Completeness of uniform metric      266
Completeness vs. Baire condition      294
Completeness vs. compactness      275
Completion      269 270
Completion, uniqueness      271
Component      159
Component in a compact Hausdorff space      235
Component vs. path component      162
Component vs. quasicomponent      163 235
Composite      18
Composite of continuous functions      107
Composite of covering maps      336
Composite of quotient maps      138
Composition of paths      322
Conclusion      7
Conjugacy class      388
Conjugate subgroups      387
Connected im kleinen      163
Connected space      147 see
Connectedness      147 see
Connectedness for subspaces      147
Connectedness in a linear continuum      152
Connectedness in R      154
Connectedness of $\mathscr{T}_f$      151
Connectedness of box topology      152
Connectedness of closure      149
Connectedness of continuous image      149
Connectedness of products      150
Connectedness vs. path connectedness      156 158
Constant path      322
Continuity after change of range      107
Continuity at a point      107
Continuity in each variable separately      112
Continuity of $f\times g$      112
Continuity of $n$th root function      111
Continuity of .maps into products      109 115
Continuity of algebraic operations in R      129 134
Continuity of composites      107
Continuity of constant function      107
Continuity of inclusion      107
Continuity of maps from quotient spaces      139
Continuity of metric      124
Continuity of restriction      107
Continuity of sums, differences, products, and quotients      129
Continuity of uniform limit      130
Continuity via bases      102
Continuity via closures      103
Continuity via nets      188
Continuity via sequences      128 190
Continuity via subbases      102
Continuity, $\epsilon - \delta$ formulation      127
Continuity, closed set formulation      103
Continuity, local formulation      107
Continuous function      102 see
Continuous image of a compact space      167
Continuous image of a connected space      149
Continuum Hypothesis      62
Contractible space      325 373
Contractible space, simple connectedness      361
Contraction      182 270
Contrapositive      8
Convergent net      187
Convergent sequence      116 127 see
Converges uniformly      129
CONVERSE      9
Convex set      152 325
Coordinate functions      109
Coset      145
Countability      46
Countability of $Z_+\times Z_+$      45 47
Countability of algebraic numbers      51
Countability of countable unions      49
Countability of finite products      49
Countability of rationals      47
Countability of subsets      47
Countability of Z      45
Countable basis      190 see
Countable basis at a point      128 190 see
Countable compactness      182 194
Countable dense subset      191
Countable dense subset in $I^1$      195
Countable dense subset in $\ell^2$      195
Countable dense subset in $\mathscr{C} (I, R)$      195
Countable dense subset in product space      195
Countable dense subset in subspace      193
Countable dense subset vs. second-countability      191 194
Countable intersection condition      234
Countable set      46 see
Countably infinite      45
Countably locally discrete      254
Countably locally finite      246
Counterimage      17
Covering      164 165
Covering dimension      302
Covering map      331
Covering map $S^1\rightarrow S^1$      335 336 393
Covering map $S^2\rightarrow P^2$      352
Covering map induces injective homomorphism      342
Covering map vs. local homeomorphism      334
Covering map, $R\rightarrow S^1$      332 393
Covering map, $R\times R\rightarrow torus$      333
Covering map, $R\times R_+\rightarrow R^2 — 0$      334
Covering map, composites      336
Covering map, products      336
Covering space      331
Covering space of topological group      342 398
Covering space vs. $\pi_1$ of base space      341 342 388
Covering space, classification      388 392 393
Covering space, equivalence      388
Covering space, existence      393
Covering space, k-fold      336
Covering space, regular      398
Covering transformation      398
cube      313
Curve      223
Curve, simple closed      375
de Morgan’s laws      11
Deck transformation      398
Decomposition space      137
Deformation retraction      373 see
Degree of a map      373
Deleted comb space      156
Deleted comb space, components      161
Deleted comb space, connectedness      157
Deleted comb space, local connectedness      162
Dense subset      191
Diagonal map      270
Diagonal set      100 201
Diameter of a set      119 177
Dictionary order relation      26
Difference of two sets      10
Dimension, topological      302 see
Directed set      187
Discrete topology      77
Disjoint sets      6
Distance      117
Distributive laws for $\cup$ and $\cap$      11
Domain      15 16
Double torus      355
Doubly punctured plane      345
Doughnut surface      334
Element of a set      4
Empty interior      293
Empty set      6
Equality symbol      4
Equicontinuity      276
Equicontinuity of closure      279 290
Equicontinuity vs. compactness      277 29U
Equicontinuity vs. total boundedness      276
Equivalence class      22
Equivalence of compactifications      239
Equivalence of covering spaces      388 392
Equivalence relation      22
Essential map      357
Euclidean metric      120 126
Euclidean space      37
Evaluation map      287
Even integer      35
Evenly covered      331
Eventually zero      52
Expansion Lemma      259
Exponents, laws of      35
F. i, c      230
Family of sets, indexed      37
Field      31
Figure eight space      345 373
Figure eight space, fundamental group      354
Final point, of a path      3 19
Fine topology on $\mathscr{C}(X Y)$      285
Fine topology on $\mathscr{C}(X Y)$ is Baire      297
Finer topology      77
Finer topology, criterion for      80
Finite axiom of choice      61
Finite complement topology      77 see
Finite intersection condition      170
Finite set      40
Finite-dimensional      302
Finiteness      40
Finiteness of finite products      44
Finiteness of finite unions      44
Finiteness of subsets      43
First category      294
First coordinate of ordered pair      13
First homotopy group      326 see
First-countability      128 190
First-countability of $R_l$      192
First-countability of $S_\Omega$      194
First-countability of metric space      128
First-countability of product      191
First-countability of subspace      191
First-countability, implies adequacy of sequences      190
First-countability, implies compactly generated      282
First-countable space      128 190 see
Fixed point      158
Fixed-point free action      357
Fixed-point theorem for $B^2$      365
Fixed-point theorem for $B^n$      369
Fixed-point theorem for $S^n$      373
Fixed-point theorem for a contraction      182 270
Fixed-point theorem for a retract of $B^2$      368
Fixed-point theorem for [0, 1]      158
Fourteen-set problem      101
Frechet compactness      178
Frobenius theorem      365 369
Function      16
Functorial properties of $h_*$      329
Fundamental group      326
Fundamental group and homotopy equivalence      371
Fundamental group of $P^2$      352
Fundamental group of $R^2 - 0$      343
Fundamental group of $R^n - 0$      344
Fundamental group of $S^1$      340
Fundamental group of $S^2$      347 350
Fundamental group of $S^n$      350
Fundamental group of a product      351
Fundamental group of double torus      355
Fundamental group of figure eight      354
Fundamental group of orbit space      357
Fundamental group of strong deformation retract      345
Fundamental group of torus      352
Fundamental group, nonabelian      354 355
Fundamental group, when abelian      330
Fundamental theorem of algebra      362
G/H      145
G/H, paracompactness      260
G/H, regularity      145
Gas-water-electricity graph      304
Gas-water-electricity graph, nonimbeddability      386
General linear group      144
General position in $R^3$      307
General position in $R^N$      309
Generalized Continuum Hypothesis      62
Geometrically independent      308
gib A      27
Graph      172
Greater cardinality      62
Greatest lower bound      27
Greatest lower bound property      27
Groupoid properties      322
Hahn — Mazurkiewicz Theorem      274
Half-open interval      84
Has n elements      40
Hausdorff condition      98
Hausdorff condition and closedness of diagonal      100 201
Hausdorff condition and uniqueness of extensions      112 241 see
Hausdorff condition for box topology      115
Hausdorff condition for manifold      225
Hausdorff condition for metric space      126
Hausdorff condition for order topology      99
Hausdorff condition for product      99 115 197
Hausdorff condition for quotient space      139 140
Hausdorff condition for subspace      99 197
Hausdorff condition for topological group      145
Hausdorff condition vs, $T_1$ axiom      99 100
Hausdorff condition vs. regularity      195 200
Hausdorff metric      279
Hausdorff space      98 see
Hilbert cube      125
Homeomorphism      104
Homeomorphism vs. continuous bijective map      106 167
Homogeneous space      144
Homomorphism, induced by a map      329 see
Homomorphism, induced by a path      327 see
Homomorphism, product      351
Homomorphism, zero      330
Homotopic maps      318
Homotopy      319
Homotopy equivalence      371
Homotopy equivalence vs. strong deformation retraction      372
Homotopy equivalence, induces isomorphism of $\pi_1$      371
Homotopy extension lemma      377
Homotopy inverse      371
Homotopy type      371
Homotopy, effect on $h_*$      369
Homotopy, equals path in $\mathscr{C}(X, Y)$      289
Homotopy, straight-line      321
Hypothesis      7
Identification space      137
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