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| Aleksandrov P.S. — Combinatorial topology. Volume 1 |
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| Предметный указатель |
 -approximation, barycentric 177
-covering 36
-displaoement 171
-mapping 170
-neighborhood 8
-net 30
(n-l)-sphere 9
Absolute boundary 41
Absolute boundary, characterization of 43
Absolute boundary, system of neighborhoods 6
Abstract complex 125
Abstract complex, simplex 121
Accumulation point 5 8
Addition formula 49
Admissible broken line 58
Admissible broken line, deformation 48 181
Affine mapping 205
Aleksandrov, P. xv xvi 18 137 170 188
Alexander xiv 65
Alexander, Pontryagin duality xiv xv
Alexandroff (see Aleksandrov)
Alexandroff axioms, closed set 4
Alexandroff for a metric space 7
Alexandroff for a neighborhood topology 6
Alexandroff for a topological space 4
Alexandroff, angle function 53
Alexandroff, arc, Jordan 39
Alexandroff, closure 5
Alexandroff, open 66
Alexandroff, open set 4
Alexandroff, partial order 26
Alexandroff, separation 16
Alexandroff, simple 39
Alexandroff, simple order 26
Baire’s theorem 7 14 29
Barycentric complex of a triangulation 144
Barycentric complex of a triangulation, approximation 177
Barycentric complex of a triangulation, barycentric star, closed 146
Barycentric complex of a triangulation, coordinates 203
Barycentric complex of a triangulation, covering dual to a triangulation 147
Barycentric complex of a triangulation, derived 131
Barycentric complex of a triangulation, dual to a simplex 144
Barycentric complex of a triangulation, mapping 172 175
Barycentric subdivision of a closed simplex 157
Barycentric subdivision of a polyhedral complex 132
Barycentric subdivision of a triangulation 78
Barycentric subdivision of order v 140
Barycentric subdivision of the dual of a complex 147
Basis for a space 6
Basis for a subspace 7
Basis, countable 7
Betti groups xiii
Betti groups in a point xiv
Betti groups, invariance of xiii
Betti number, one-dimensional 68
Bicompacta of weight  , characterization of 18
Bicompacta of weight , theorems on 17 18
Bicompactum 17
Bicompactum, characterization of 18
Bicontinuous mapping 10
Body of a complex 71 136
Body of a triangulation 71
Body, convex 208
Boundary of a closed n-cell 167
Boundary of a convex polyhedral domain 120
Boundary of a set 5
Boundary of a simplex 119
Boundary of a surface 76
Boundary, absolute 41
Boundary, elements of a triangulation of a surface 77
Boundary, outer, of a star 73 126
Boundary, point of a set 5
Boundary, point of a surface 76
Boundary, regular 41
Branch point of an elementary curve 66
Brouwer 17 37 42 155 156 170
Brouwer’s example 42
Brouwer’s example, Urysohn theorem 17
Cantor 10
Cantor, perfect set 13 15 18 40 196
Cantorian manifold 199
Cantorian manifold of a point 137
Cantorian manifold of a simplex 156
Cantorian manifold of an element of a subdivided polyhedral complex 139
Cantorian manifold, carrier 156
Cantorian manifold, carrying plane of a convex set 210
Cauchy definition chain of uoinploxos 83
Cauchy definition of a star 126
Cauchy definition of continuity 9
Cauchy definition of continuity, center of a closed barycentric star 146
Cauchy definition of continuity, sequence 29
Cauchy definition of projection 214
Cauchy definition of semi-stnrH 84
Cauchy definition of sets 14
Cauchy definition of simplexeB 200
Cauchy definition of subdivisions 191
Cauchy definition of system of muss points 204
Cauchy definition of triangles 84
Cauchy definition, central subdivision of a polyhedral complex 141
Cauchy definition, centroid of a simplex 213
Chain of sets 14
Chained system of sets 14
Characterization of 17 18
Closed barycentric star 146
Closing a hole with a Mobius band 92
Closure axioms 5
Closure axioms of a set 5 6 7
Closure axioms of a simplex 118
Coherent orientation 94
Cohomology xiii
Combinatorial boundary of a simplex 119
Combinatorial closure in a complex 121
Combinatorial closure in a partially ordered set 27
Combinatorial closure of a barycentric star 145
Combinatorial closure of a convex polyhedral domain 120
Combinatorial closure of a simplex 119
Combinatorial closure of a simplicial complex 122
Combinatorial closure of a subcomplex 126
Combinatorial closure topology, fundamental hypothesis of 150
Combinatorial closure topology, method of 33
Combinatorial closure type of simplicial complexes 124
Combinatorial closure, sum of simplexes 118
Compact Hausdorff space 17
Compact Hausdorff space, metrizable space 17
Compact Hausdorff space, space 17
Compacta, theorems on 17
Compactness 17
Compactness, local 24
Compactum 17
Complete metric space 29
COMPLEX 71
Complex in a triangulution 71
Complex, abstract 125
Complex, connected 71 152
Complex, infinite 158
Complex, polyhedral 110
Complex, pure 72 200
Complex, simplicial 122 125
Complex, skeleton 78 121
Complex, strongly connected 72 200
Complex, topological 149
Complex, unrestricted 121 122 125
Component of a complex 152
Component of a space 15
Component, regular, of an elementary curvc 67
Cone 214
Cone-complex 134
Connected complex 71 152
Connected complex, doublet 13 16
Connected complex, space 13
| Connectedness 13
Connectedness of  14
Connectedness of a convex set 14
Connectedness of the real line 13
Connectedness, local 41
Connectedness, strong 72 199 200
Connectivity of a complex 69
Connectivity of a surface 100
Connectivity of a triangulation 99
Connectivity of an elementary curve 68
Connectivity, invariance of 100
Contact point 5 6 8
Continuous family of mappings 32
Continuous family of mappings, functions in normal spaces 17
Continuous family of mappings, image of a connected space 15
Continuous family of mappings, image of the Cantor perfect set 18 196
Continuous mapping 9
Continuous mapping, decomposition of a compactum induced by 18
Continuous mapping, extension of 17
Continuous mappings of bicompacta 18
Continuous mappings, theory of xiv
Contour of a surface 76
Convergence, sequential 8
Convex body 208
Convex body, polyhedral domain 212
Convex body, set 208
Convex hull 210
Convex polyhedral domain 212
Coordinates in a topological product 10
Coordinates, barycentric 203
Countable basis 7
Countable basis, weight 7
Covering 4
Covering, closed 32 36
Covering, irreducible 189
Covering, Lebesgue numbers of a closed 35
Covering, open 32
Covering, order of 32
Covering, simple 37
Coverings, similar 33
Cross cut 82
Curve 39
Curve, elementary 66
Curve, Jordan 39
Curve, simple closed 39
Curved triangulation 73
Cut 101
Cut line 82
Cut line, closed 100
Cut line, interior closed 82
Cut line, manifold 24 150
Cut line, manifolds, examples of 24
Cut line, n-cell 167
Cut line, nonseparating 00
Cut line, one-sided closed 86
Cut line, one-sided cut line 86
Cut line, open 82
Cut line, path 47
Cut line, polyhedral domain 212
Cut line, polyhedral manifold 150
Cut line, projection 214
Cut line, separating 00
Cut line, set 4 7
Cut line, simplex 212
Cut line, solid n-sphere 8
Cut line, subcomplex 71 126
Cut line, surface 73 76
Cut line, topological n-manifold 24
Cut line, two-sided closed 85
Cut line, two-sided cut line 85
Cut operation 86
Cycle of a 1-complex 69
Cycle of a 1-complex, relative xiv
Cycle of a 1-complex, simple 68
Cycle of a 1-complex, singular xiii xiv
Cycle of a 1-complex, true xiii xiv
Cycle of an elementary curve 68
Cyclic star 73
Decomposition of an elementary curve 67
Decomposition of an elementary curve, space 19
Deformation 32
Deformation, admissible 48 181
Degenerate n-simplex 116
Degenerate n-simplex, set 16
Degree of a mapping 52
Dense 5
Diameter of a metric space 8
Difference of sets 2
Dimension number of a complex 71 155
Dimension number of a convex set 210
Dimension number of a polyhedron 155
Dimension number of a simplex 116 155
Dimension number of a simplicial complex 122
Dimension number of a topological complex 149
Dimension number of a triangulation 118
Dimension of a bicompactum 36 37 38
Dimension of a compactum 37 38 177 179 197
Dimension of a complex 71
Dimension of a nerve 129
Dimension of a simplex 116
Dimension of a simplicial complex 122
Dimension of a skeleton complex 79
Dimension of a triangulation 118
Dimension of an abstract simplex 122
Dimension, inductive 187
Dimension, intuitive meaning of 37
Disconnect 39
Discrete spaces 16 28
Discrete spaces and partially ordered sets 28
Disorienting sequence 06
Displacement 171
Distance 7 9
Distance in Euclidean space 8
Distance in Hilbert space 9
Distance in space of continuous mappings 31
Distance, between a point and a set 7
Domain 14
Doublet 13
Doublet, connected 13
Doubling of a three-dimensional ring 22
Dual of a barycentric star 144
Dual of a complex 147
Dual of a partially ordered set 27
Dual of a simplex 144
Dual of a triangulation 144
Dual of a triangulation and homology dimension xv
Dual of a triangulation, duality laws xv
Dual of a triangulation, subcomplexes 147
Dyadic discontinuum 13
EDGE 71
Eilenberg xv
Elementary curve 66
Elementary subdivision of a complex 67
Elementary subdivision of a polyhedral complex 141
Elementary subdivision of a triangulation 77
Endpoint of an elementary curve 66
Equivalence of open and closed coverings 33
Essential mapping 181
Euclidean n-space 8
Euler characteristic of a 1-complex 67
Euler characteristic of a triangulation 99
Euler characteristic of an elementary curve 67
Euler theorem 69 99 105
Extension of a continuous mapping 17
Extension of an affine mapping 208
Face of a convex polyhedral domain 213
Face of a simplex 116
Faces, opposite 117 212
Family depending on a parameter 4
Fixed point theorem 166 168
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