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| Cairns S.S. — Introductory topology |
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| Предметный указатель |
Abelian (see Group)
Adjacent 112
Affine transformation 68
Aggregate 41
Alexander duality theorem 180
Approximating complex 143
Approximating simplex 143
ARC 186
Arithmetical continuum 48
Barycenter 73 83
Barycentric coordinates 70
Barycentric subdivision 83
Base, Betti 119
Base, connectivity 122
Base, homology 119
Base, of a topology 52
Base, torsion 119
Basis 222
Betti, base 119
Betti, group 97
Betti, number 7 97 228
Betti, relative (or mod L) 176
Betti, singular 132
Bolzano — Weierstrass theorem 59
Boundary of a chain 94
Boundary of a set 53
Boundary of a simplex 72
Boundary of a surface 15
Boundary, chain 92
Boundary, complex 100
Boundary, face 77
Boundary, mod 2 121
Boundary, point 53
Boundary, simplex 72
Bounded 57
Brouwer dimension 62 136
Brouwer’s fixed-point theorem 137
Carrier 133
Cell, abstract 78
Cell, boundary of 87
Cell, chain 165
Cell, complex 165
Cell, dimension of 78
Cell, face of 87
Cell, homology 165
Cell, polyhedral 87
Chain 92
Chain of a complex 112
Chain, boundary of 92 94
Chain, cell 165
Chain, coboundary 122
Chain, equality of 130
Chain, group 92 95
Chain, singular 130
Characteristic 109 118
Characteristic, mod L 177
Circuit 6
class 41
Class of mappings 152
Class, equivalence 44
Class, residue 218
Closed interval 48
Closed mapping 55
Closed set 53
Closed surface 15
Closure 53
Coboundary 123
Coboundary, chain 122
Coboundary, operator 122
Cocycle 123
Coherently oriented 93 112
Cohomology, class 124
Cohomology, group 124
Cohomology-independent 125
Collection 41
Column vector 223
Combinatorial equivalence 83 88
Combinatorial homotopy 195
Compact 59
Compactum 59
Complement 42
COMPLEX 74
Complex of a chain 142
Complex, abstract 77
Complex, boundary 100
Complex, cell 165
Complex, cone 154
Complex, denumerable 77
Complex, dimension of 77
Complex, finite 74 77
Complex, floor 145
Complex, generalized 78
Complex, infinite 75
Complex, isomorphic 80
Complex, linear 77
Complex, oriented 92
Complex, polyhedral 87
Complex, realization of 78
Complex, roof 145
Complex, singular 142
Complex, subdivision of 87
Complex, topological 76
Component 76 77
Components, contra variant 231
Components, covariant 232
Composition of mappings 43
Cone complex 154
Congruent mod 220
Congruent mod m 218
Connected 76 77
Connected graph 4
Connected surface 15
Connected, arc wise 187
Connected, simply 191
Connectivity, base 122
Connectivity, group 121
Connectivity, number 121
Continuity 51
continuous 49 50 51
Continuous at a point 54
continuous curve 185
Continuous on a space 54
Continuum 48
Converge 54
Convex 66
Coordinates, affine 68
Coordinates, barycentric 70
Coordinates, rectangular Cartesian 68
Coordinates, skew 68
Coset 220
Countable 44
Cover 205 209
Covering 59
Covering complex, universal 210
Covering pair 177
Covering path 209
Covering set 205
Covering space 205
Covering,  -covering 61
Covering, closed 59
Covering, infinite 205
Covering, k-fold 205
Covering, of mesh 61
Covering, open 59
Covering, order of 62
Covering, simple 64
Crosscap 22
Curve, closed 186
Curve, Peano 186
Curve, simple 186
| CYCLE 94
Cycle, group 94 95
Cyclomatic number 7
Decomposition 45
Deformation 152 187
Deformation, homotopic 151
Deformation, path 151
Denumerable 43
Diagonal 136
Diameter 57
DIMENSION 65
Dimension, Brouwer 62 136
Dimension, number 65 67
Dimension, numerical 67
Disjoint 42
Distance, between two sets 57
Distance, Euclidean 50
Domain 42
Dual bases 233
Dual homomorphisms 235
Duality theorem, Alexander 180
Duality theorem, Lefschetz 179
Duality theorem, Poincare 173
EDGE 19
Edge, free 19
Edge, paired 19
Edge, path 193
Empty 41
Equivalence, class 44
Equivalence, combinatorial 83 88
Equivalence, relation 44
Euclidean space 48 50
Euler — Poincare characteristic 109 118
Euler’s theorem 12
Extension 42
Face 77
Face of a simplex 72
Face, boundary 77
Factor group 220
Fixed point 136
Fixed-point theorem 137
Floor complex 145
Function (see Mapping)
Fundamental group 185 189 190 196
Genus 109
Graph 4
Graph of a function 51 136
Graph of a relation 45
Graph, connected 4
Graph, linear 4
Group of order m 218
Group, abelian 215
Group, addition 215
Group, additive 215
Group, axioms 215
Group, basis 222
Group, Betti 97 176
Group, bounding cycle 95 166
Group, chain 92 95
Group, cobounding cocycle 166
Group, cocycle 166
Group, cohomology 124 166
Group, combinatorial 196
Group, commutative 215
Group, connectivity 121
Group, cycle 94 95 165 166
Group, cyclic 218
Group, difference 220
Group, factor 220
Group, finitely generated 216
Group, free abelian 217
Group, free cyclic 218
Group, free multiplicative 217
Group, fundamental 185 187 189 190
Group, generators 216
Group, homology 96 166
Group, invariant 219
Group, inverse element 215
Group, local 159
Group, made abelian 196
Group, mod 2 121
Group, multiplication 215
Group, multiplicative 215
Group, Poincare (see Group fundamental)
Group, product, direct 221
Group, quotient 220
Group, relations 217
Group, relative (or mod L) 176
Group, relative cycle 176
Group, singular 132
Group, structure 219
Group, torsion relative 176
Group, unit element 215
Half-space 86 111
Half-space, closed 86
Half-space, open 86
Handle 25
Heine — Borel theorem 60
Homeomorphic 54
Homeomorphism 54 55
Homeomorphism, linear 69
Homologous 96
Homology, base 119
Homology, cell 165
Homology, class 96
Homology, group 96
Homology, relative 175
Homology, singular 131
Homology-independent 97
Homomorphism 219
Homomorphism, dual 235
Homotopic, chains 152
Homotopic, complexes 152
Homotopy 152
Homotopy, class 152 189 196
Homotopy, combinatorial 195
Image 42
incidence 77
Incidence, matrix 114
Incidence, normal 115
Incidence, number 114 165
Incidence, relation 77
incident 17 75
Independent, cohomology 125
Independent, homology 97
Independent, linearly 71 97
Induced homeomorphism 81
Induced mapping 82
Induced orientation 93
Induced topology 53
Inner point 53 72
Integral module 231
Integral module, basis 231
Integral module, initial 231
Intersection 41 42
Interval, closed 48
Interval, half-open 49
Interval, open 48
Inverse image 43
Inverse mapping 43
Isomorphic complexes 80
Isomorphism 80 219
Jordan theorem 182
Jordan — Brouwer theorem 182
Kernel 220
Klein bottle 38
Kronecker delta 68 223
Lebesgue number 64
Lebesgue’s lemma 64
Lefschetz duality theorem 179
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