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| Eilenberg S., Steenrod N. — Foundations of Algebraic Topology |
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| Предметный указатель |
Abstract, category 108
Abstract, cell complex 156
Acyclic, carrier 171
Acyclic,complex 170
Additive functor 121
Adjusted homology sequence 245
Admissible, category 5
Admissible, map 306
Algebraic, homotopy 170
Algebraic, map 170
Alternating chain complex 174
Associated LC-theory 271
Augmented, complex 169
Augmented, singular complex 190
Automorphism of a simplex 82
Axioms for cohomology 14
Axioms for homology 10
Barycenter 61
Barycentric, coordinates 55
Barycentric, subdivision 61 63 177
Base 133
Base point 17
Betti number 52 138
Bihomomorphism 160
Borsuk's separation criterion 302
Boundary 56 74 90
Boundary of a chain 88
Boundary operator 10
Boundary operator of a couple 127
Boundary operator of a traid 35
Boundary operator of a triple 24
Bounded 269
Brouwer fixed point theorem 301
c-functor 114
C.S. 14
Canonical, base 139
Canonical, imbedding 55
Canonical, map into a nerve 286
Carrier 170 234
Carrier, compact 255
Cartesian product 67 131
Category 109
Category of all pairs 5
Category of compact pairs 5
Category of locally compact pairs 5
Category of triangulable pairs 76
Category with couples 114
Cech homology groups 237
Cech homology groups, system 237
cell 44
Cell, complex 156
Cell, relative 311
Chain 84
Chain, complex 124
Chain, homomorphism 84
Chain, homotopy 129
Circuit 106
Closed, covering 233
Closed, path 313
Closed, sot 4
Closure 4
Coboundary 92
Coboundary of a cochain 90
Coboundary operator 14
Coboundary operator of a triad 37
Coboundary operator of a triple 29
Cochain 86
Cochain, complex 125
Cocycle 92
Coefficient group 17 18
Cofinal 212
Cofinal subsystem 214
Cohomology functor 112
Cohomology group 13
Cohomology group of a chain complex 153
Cohomology group of a complex 92 166
Cohomology group, Cech 237
Cohomology group, singular 188
Cohomology sequence of a, pair 14
Cohomology sequence of a, triad 37
Cohomology sequence of a, triple 29
Cohomology theory 13
Cohomology theory of chain complexes 153
Cohomology theory of complexes 166
Cohomology theory, Cech 237
Cohomology theory, singular 188
Cohomotopy groups 49
Collapsible 18
Compact 4
Compact carriers 255
Compactification 270 277
Complement 74
Completely regular 276
Complex, finite 56
Complex, infinite 74 162
Complex, locally finite 75 183
Component 254
Composition of functions 3
Contiguous 164
continuous 4
Continuous homology theory 260
Contractible to a point 30
Contravariant,  -functor 116
Contravariant,  -functor 117
Contravariant, functor 111
Coordinate 131
Countercompact 269
Couple 114 126
Covariant, -functor 116
Covariant, -functor 115
Covariant, functor 111
Covering 233
Covering of a pair 234
Covering theorem 187
cube 276
CYCLE 90
Cylinder 210
Deformation, chain 129
Deformation, retract 30
Degenerate chain 173
Degree of a map 304 306
Development 288
Diagonal form 139
Diagonal form, map 67
Dimension of a complex 56
Dimension, axiom 12
Direct limit 220
Direct product 131
Direct sum 8 10 32 132
Direct system 212
Direct, couple 126
Direct, homology groups 184
Direct, system of upper sequences 224
Directed set 212
Distance in a simplex 55
Domain 109
Domain of integrity 52
Duality 14
Elementary, chain 163
Elementary, subdivision 74 75
Enlargement 261
EQUIVALENCE 109
Equivariant 73
Equivariant, homology groups 209
Essential 299
Euclidean complex and simplex 73
Euler characteristic 53
Exact sequence of groups 8
Exactness axiom 11
Exactness axiom, partial 253
| Excision axiom 11 12
Excision map 12 130
Excision map for complexes 165
Excision map, generalized 117
Excisions of various types 267
Ext 161
Face of a singular simplex 186
Face sequence 9
Face, factor, complex 125
Face, of a simplex 55
Finite cochains 183
Five lemma 16
Fixed point theorem 301
Formal homology theory 166
Free, base 133
Free, module 134
Full, subcategory 110
Full, subcomplex 70
functor 111
Fundamental theorem of algebra 307
Generalized excision 117
Generate 133
Grating 254
Group 6
Group of homomorphisms 147
Group of operators 73
h-category 117
h-functor 118
H.S. 11
Hausdorff space 4
Hexagonal lemma 38
Homeomorphic 17
Homologically trivial 22
Homology functor 112
Homology group 10
Homology group of a chain complex 125 151
Homology group of a chain mapping 169
Homology group of a complex 90 166
Homology group of a triad 203
Homology group, Cech 237
Homology group, equivariant 209
Homology group, singular 188
Homology sequence of a, pair 11
Homology sequence of a, triad 35
Homology sequence of a, triple 25
Homology theory 10
Homology theory for normal spaces 282
Homology theory, Cech 237
Homology theory, continuous 260
Homology theory, equivariant 209 for
Homology theory, locally compact spaces 271
Homology theory, singular 188
Homomorphism 7
Homomorphism of a sequence of groups 9 15
Homotopic 6
Homotopic, chain maps 129
Homotopy 6
Homotopy axiom 11 12
Homotopy equivalence 29 117
Homotopy groups 48 207
Homotopy, inverse 117
Horn 147 152
Identity 108
identity map 3
Image 7 9
Imbedding 61
In variance, of dimension 302
In variance, of domain 303
Incidence isomorphism 79 80
Incidence isomorphism, number 156
Inclusion map 3
INDEX 169
Index of a singular chain 190
Indexed family of sets 233
Induced homomorphism 10 14 239
Inessential 299
Infinite, complex 74
Infinite, triangulation 75
Infinitely divisible 159
Injection 8 132 214
Injective representation 8 133
Interior 4
Intersection of a nested system 260
INV 258
Invariance 180
Invariant 73
Invariant under relative homeomorphisms 266
Inverse homology group 184
Inverse limit 215
Inverse system 213
Inverse system of factor groups 228
Inverse system of lower sequences 224
Inverse system of subgroups 228
Isomorphism 7 9
Join 74 172 192
Kernel 7 9
Lattice of a pair 4
LC-theory 271
Lebesgue number 65
Line segment 72
Linear 6
Linear imbedding 61
Linear independence 52 72 133
Linear map 57 60
Linear metric 61
Linear singular simplex 192
Linear subspace 6
Locally Euclidean 303
Locally finite complex 75 183
Lower cap 44
Lower sequence of groups 8
Main isomorphism 94
Manifold 311
MAP 3
Map defined by a map 3
Map, linear 57 60
Map, simplicial 58 60
Mapping cylinder 210
Mappings 109
Maps of inverse and direct systems 213
Mayer homology groups 182
Mayer — Vietoris, formula 53
Mayer — Vietoris, sequence 37 39 42 43
mesh 60
Mesh of a covering 251
Metric topology 75
Module over a ring 6
Monomial 308
Multiplicative system 108
Natural, equivalence 112
Natural, homomorphism 7 10
Natural, transformation 112
Nerve 234
Nested system 260
Nonorien table 313
Nonorien table, circuit 106
Norm 44
Normal pair 278
Normal space homology theory 282
Objects 109
Onto 7 9
Open covering 233
Open set 4
Open simplex 56
Open star 57
Operator group 73
Ordered, chain complex 163
Ordered, complex 67
Ordered, simplex 55
Orientable 313
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