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| Авторизация |
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| Dugunji J. — Topology |
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| Предметный указатель |
First uncountable ordinal 54
Fixed point 305
Fixed-point theorem in complete metric spaces 305
Fixed-point theorem, Brouwer’s 341 353
Fixed-point theorem, Tychonoff 414
Flat 412
Foundation, axiom of 20 42
Fox, R.H. 275
Free union 127 132
Freudenthal, H. 314 350
Function 10
Function space 257
Function space, admissible topology 274
Function space, c-topology 257
Function space, conjoining topology 274
Function space, metric topology 269
Function space, p-topology 272
Function space, proper topology 274
Function space, splitting topology 274
Function, equality of two 11
Function, range and domain of 10
Fundamental group 381 388 389
Fundamental theorem of algebra 342
G-hereditary property 206
G.,-set 74
Gauge 198
Gauge derived from a map 198
Gauge induced in cartesian product 198 200
Gauge space 199
Gauge, separating family of 198
Gelfand — Kolmogoroff theorem 287 289
Gelfand, I. 287
General extension theorem 149
General position 412
Generalized Continuum Hypothesis 49
Generalized convergence 235
Geodesic distance 206
Geometric complex 418
Geometric nerve 172
Geometric realization 172
Germs of continuous maps 422
Godel, K. 21 49
Grating 177
Group 410
H-equivalent H-structures 382
H-homomorphism 381
H-isomorphism 382
H-space 383
H-structure 379
H-structure with inversion 386
H-structure with unit 384
H-structure, H-abelian 388
H-structure, H-associative 387
H-structure, induced on components 381
H-structure, induced on function space 381 391
H-structure, principal component of 380
Halo 327
Hamel basis 35
Hanai, S. 235
Hausdorff metric 205 253
Hausdorff space 137
Hausdorff, F. 286
Hilbert cube 192
Hilbert space 192
Holladay, J.C 284
Homeomorphism 87
Homeomorphism type 88
Homotopic spaces 365
Homotopy 315
Homotopy class 317
Homotopy equivalence 366
Homotopy equivalence (pair) 368
Homotopy extension property 326
Homotopy groups 388 389
Homotopy inverse 366
Homotopy rel A 321
Homotopy type 365
Hopf fiber structures 407
Hopf map 408
Hopf, H. 352 407 408
Hurewicz fibration 393 395
Hurewicz, W. 314 396 400
Ideal, dual 213
Ideal, in ring 288
Ideal, in well-ordered set 36
Ideal, maximal 288
Identification 121
Identification map 121 123
Identification of subset to point 125
Identification topology 120 262
Identification topology in cartesian products 262 ff.
identity map 11
Identity relation 14
Implicit function theorem 306 313
Inclusion map 11
Indexing set 8
Indiscrete topology 63
Induced fiber structure 395
Induced gauge structure in cartesian products 198 200
Induced map of function spaces 259
Induced set map 11
Induction, transfinite 40
Inductive limit space 421
Inductive property 180
Inductive spectrum 420
Infinity, axiom of 20
Initial interval 36
Interior 71
Interior, operator 74
Intersection 3 8
Invariance of dimension number 350 359
Invariant, algebraic 367
Invariant, positional 355
Inverse image 11
Inverse limit map 431
Inverse limit space 427
Inverse spectrum 427
Inverse spectrum, generalized 434
Irreducible covering 160
Irreducible map 394
Isolated point 92
Isometry 285 314
Isomorphism of metric spaces 285
Isomorphism of well-ordered sets 37
Janiszewski, S. 362
Join 128 135
Joint topological invariant 257
Jones, F.B. 144
Jordan curve theorem 362
Jordan separation theorem 358
k-space 248 263
Kneser, H. 58
Kolmogoroff, A. 287
Krull’s Theorem 36
Kuratowski, C 112 286 363
Larger topology 64
Lattice 57
Lattice, complete 91
Lavrentieff, M. 314
Lebesgue non-measurable set 36
Lebesgue number 234 (196)
Lexicographic order 57
Lifting function 396
Lifting function, extended 397
Lifting function, regular 396
Lifting of map 393
Limit of filterbase 212
Limit of net 210
Limit ordinal 44
Limit space, direct 421
| Limit space, inverse 427
Lindelof space 174
Linear T-approximation 344
Linear topological space 413 ff.
Linear topological space, locally convex 414
Linear topological space, normed 414
Linearly independent 412
Load 122
Local Hurewicz fibration 403
Locally compact 237
Locally connected 113 125
Locally convex linear topological space 414
Locally equiconnected space 334 405
Locally Euclidean space 364
Locally starring sequence 169
Locally trivial fiber structure 404 ff.
Loop 376
Loop space 377 382
Lower semi-continuous 84 170
Lusternik — Schnirelmann theorem 349
MAP 10 14
Map, closed 86
Map, composition of 12
Map, constant 11
Map, continuous 79
Map, embedding 89
Map, extension of 13
Map, identity 11
Map, inclusion 11
Map, injective 13
Map, lower semi-continuous 84
Map, open 79 86
Map, perfect 235
Map, relation-preserving 16
Map, restriction of 12
Map, surjective 13
Map, upper semi-continuous 84
Mapping cylinder 368
Mapping of direct spectra 422
Mapping of inverse spectra 430
Maximal element 30
Maximal filterbase 218
Maximum modulus theorem 96
Mazur, B. 358
Mazurkiewicz, S. 308
Meager set 250
Metacompact 229
Method of complements 6
Metric 181
Metric space 183
Metric topology in function spaces 269
Metrizable space 183
Metrization of topological spaces 194—196 200 207 233 235 253
Michael, E.A. 163 165 191 206
Minkowski’s inequality 182
Monomorphism of well-ordered sets 37
Montgomery, D. 207
Morgenstern, D. 301
Morita, K. 174 196 255
Morse, M. 358 374
Mrowka, J. 244
Nagata — Smirnov theorem 194
Nbd (neighborhood) 63
Nbd filterbase 211
Nbd of equicontinuity 266
Nbd-finite family 81
Nbd-finite subcovering 223
Nbds, complete system of 67
Nerve 172
Nerve, geometric 172
Net 210
Non-meager 250
Non-vanishing vector field 342
Norm 414
Normal space 144
Normal, completely 146
Normal, perfectly 148
Normed linear space 414
Novak, J. 244 245
Nowhere analytic functions 301
Nowhere dense 92 250
Nowhere differentiable functions 300
Null set 2 19
Nullhomotopic 315 317 318
Number, cardinal 46
Number, ordinal 42
One-to-one map 13
Onto map 13
Open map 86
Open relation 126
Open set 63
Ordered pair 7
Ordered simplex 336
Ordering, lexicographic 57
Ordering, partial 30
Ordering, pre- 29
Ordering, total 30
Ordering, well 31
Ordinal 31
Ordinal number 42
Ordinal space 66
Ordinal, comparability of 38
Ordinal, first uncountable 54
Ordinal, limit 44
p-load 122
P-topology 272
Pair homotopy equivalence 368
Pair homotopy inverse 366
Pair homotopy type 368
Pair nomotopic spaces 368
Pairing, axiom of 19
Paracompact space 162
Paracompact, countably 178
Parallelotope 155
Parameter transformation 377
Parametric representation of curves 101
Partial ordering 30
Partial ordering by inclusion 30
Partition of set 13
Partition of unity 169
Partition of unity subordinated to a covering 170 173
Passage to quotient 17
Path 114 376
Path space 377
Path, inverse of a 376
Path, rectifiable 206
Path-connected 114
Paths, equivalent 378
Paths, product of 376
Peano curve 105
Perfect map 235
Perfect set 92
Perfectly normal 148
Picard successive approximations 305
Piecewise definition of map 83
Poincare, H. 343
Point-finite covering 152
Pointwise convergence, metrizability of 273
Pointwise convergence, topology of 272
Polytope 172 418
Polytope, triangulation of 418
Popisil, B. 244
Positional bound 355
Positional invariant 355
Postnikov, M.M. 368
Power set 10 19
Power set, axiom of 19
Precise refinement 161
Precompact 298
Preordering 29
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