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| Авторизация |
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| Aleksandrov P.S. — Combinatorial topology. Volume 1 |
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| Предметный указатель |
Frontier of a simplex 118
Fundamental group xv
Fundamental group, hypothesis of combinatorial topology 160
Fundamental group, sequence 29
Fundamental group, theorem of surface topology 110
Gawehn 73
Gawehn of an orientable surface 108
Gawehn, general position 204
Gawehn, genus of a nonorientable surface 108
Gawehn, geometric partial order 26
Gawehn, geometric realization of a nerve 131
Glezerman xv
Half-space, closed 203
Half-space, open 202
Handle of the first kind 93
Handle of the second kind 93
Hauptvermutung 160
Hausdorff space 16
Hausdorff space, compact 17
Hausdorff space, normal 16
Hilbert parallelotope 9 13 171 174 179
Hilbert parallelotope, space 9 171
Homeomorphic spaces 10
Homological manifold xiv
Homology dimension xiv 170
Homology dimension, relative xiv
Homology theory xiii
Homology theory of bicompacta xiv
Homology theory of compacta xiv
Homology theory, topological invariance of xiii
Homotopic mappings 32 63
Homotopy xv
Homotopy, classes of mappings 32
Homotopy, groups xv
Hopf, H. xiii xiv xv
Hurewicz, xv 200
Identification 20 124
Identification of elements of a triangulation 79
Identification of partially ordered sets and discrete spaces 29
Identification of points of a space 20
Identification of the first kind 93
Identification of the second kind 93
Identification of vertices of a simplicial complex 125
Identification of vertices of a skeleton complex 79
Identifications, examples of 20 80
Image 3
Imbedding theorems 18
Incident simplexes 117
Index of a point relative to a closed path 47
Index of a point relative to a continuous mapping 47
Index of a point relative to a mapping of a circumference 62
Index of a point relative to an oriented Jordan curve 51
Indexed set 3
Indexed set, system of sets 3
Induced orientation 94
Inductive dimension 187
Inductive dimension at a point 187
Infinite dimension 37
Infinite dimension, triangulation 168
Interior closed cut 82
Interior closed cut of a set 5
Interior closed cut, element of a surface 77
Interior point 5
Interior point of a convex set 210
Interior point of a set 5
Interior point of a surface 76
Intersection of sets 2
Intersections, theory of xiv xv
Invariance of connectivity 100
Invariance of dimension number of .ff 156 163
Invariance of interior points 74 166 164
Invariance of orientability 95
Invariance of the Euler characteristic 99
Inverse image 3
Isolated point 5
Isomorphism of abstract complexes 126
Isomorphism of simplicial complexes 124
Isomorphism of skeleton complexes 79
Jordan arc 39
Jordan arc, curve 39
Jordan arc, theorem 39
Klein bottle 81 97 114
Knaater 166
Kuratowski 156
Lebesgue 37
Lefschetz xiv xv
Lefschetz, Hopf formula xiv
Lemma 35 162
Limit point 5 8
Linear closure of planes 204
Linear independence of cycles 68
Linear independence of points 203
Linking theory xiv
Liomeomorphism 10
Local compactness 24
Local compactness, connectedness 41
Major star 144
Manifold, homological xiv
Manifold, topological 24
Manifolds with boundary xiv
Mapping 3
Mapping of order n 196
Mapping, affine 205
Mapping, bicontinuous 10
Mapping, continuous 9 170
Mapping, essential 181
Mapping, into 3
Mapping, normal, of degree a 52
Mapping, similarity 26
Mapping, simple 50
Mapping, simplicial 79 123
Mappings, composition of 3
Mappings, uniform convergence of 10
Mazurkiewicz 156
Meobius 204
Meobius, band 80 91 96
Meobius, modification of a closed covering 164
mesh 157
Metric 7
Metric space 7
Metric space, complete 29
Metric space, locally connected 41
Metric space, totally bounded 30
Metrizable space 10
Metrizable space, compact 17
Metrization theorems 18
Moise 150
n-cell 167
n-manifold 24
n-simplex 116
n-sphere 9 24 1
N-sphere, complex 67
N-sphere, covering 32
N-sphere, cut 82
N-sphere, element 67
N-sphere, manifold 24 25
N-sphere, mapping 3
N-sphere, n-cell 167
N-sphere, one-dimensional Betti number of nn elementary curve 68 1
N-sphere, open cone 134
N-sphere, projection 214
N-sphere, set 4
N-sphere, simplex 212
N-sphere, solid n-sphere 9
N-sphere, stars of a triangulation 138
N-sphere, subcomplex 71 126
natural order 26
Natural order, topology of a metric space 8
Negative affine mapping 206
Neighborhood 5
| Neighborhood in a decomposition space 19
Neighborhood in a topological product 11
Neighborhood, Spherical 8
Neighborhood, system 6
Neighborhood, topology 6
Neighborhoods, absolute system of 6
Nerve of a covering 129
Nerve of a coverings, examples of 129
Non-singular affine mapping 205
Noncoherent orientation 94
Nonorientable surface 95
Nonorientable surface, triangulation 94
Nonseparating cut 90
Nonseparating cut, subcomplex 99
Normal closed nonorientable surface of genus p 109
Normal closed orientable surface of genus p 109
Normal hausdorff space 16
Normal mapping of degree to 52
Normal simple surface with r contours 106
Numbers of a closed covering 35
Operation 5
Opposite faces of a simplex 212
Order axioms 26
Order axioms, partial 26
Order axioms, simple 26
Order of a covering 32
Order of a finite system of sets 4
Order of a mapping 196
Order orientable surface 95
Order, triangulation 94
Orientation of a Jordan arc 45
Orientation of a Jordan curve 46
Orientation of a triangle 94
Orientation of a triangulation 94
Outer boundary of a barycentric star 144
Outer boundary of a star 73 126
P-face 212
P-face, Fflastersatz 37 155 162
Partial order in a complex 71 118
Partially ordered set 25
Phase space 13
Plane of support 213
Plane, carrying 210
Pliicker coordinates 24
Poincars xiv xv
Point set boundary of a simplex 118
Polyhedral complex 119
Polyhedron 71 118 136
Polyhedron, triangillion of 137
Pontryagin xiv xv 128 134
Positive affino mapping 206
prism 135
Products, theory of xv
Projection 214
Proportional sequences 22
Pure complex 72 200
R-face 117
R-plane 202
r-simplex 212
ratio 22
Real line 7 13
Reduction of holes 90
Reduction of holes by means of a handle 93
Refinement of a system of sets 32
Regular boundary 41
Regular boundary, component of an elementary curve, point of an elementary curve 66
Regular boundary, subdivision of a tri angulation 78
Relative cycles xiv
Relative cycles, homology xiv
Relative cycles, topology 5
Retraction 172 174
S, examples of 24
Schmidt, E. 39
Semi-cyclic star 73
Semi-star 83
separate 39
Separation axioms 16
Separation axioms of two points 55
Sequential convergence 8
Similar coverings 33
Similar coverings, partially ordered sets 26
Similarity mapping 26
Simple arc 39
Simple arc, closed curve 39
Simple arc, complex 68
Simple arc, covering 37
Simple arc, mapping 50
Simple arc, nerve 129
simplex 116 212
Simplex, abstract 121
Simplex, boundary of 119
Simplex, carrier of 156
Simplex, centroid of 213
Simplex, closed 118
Simplex, degenerate 116
Simplex, dimension of 116
Simplex, face of 116 116
Simplex, opposite faces of 117
Simplex, skeleton of 116
Simplex, topological 149
Simplex, triangulation of a closed 156
Simplex, vertices of 116
Simplexes, chain of 200
Simplexes, incident 117
Simplicial complex 122 125
Simplicial complexes, examples of 122
Simplicial mapping of a polyhedron 139
Simplicial mapping of a simplicial complex 123
Simplicial mapping of a skeleton complex 123
Singular affine mapping 205
Singular affine mapping, point of an elementary curve 66
Skeleton 78 121 129
Skeleton of a degenerate simplex 116
Skeleton of a simplex 121
Skeleton of a simplicial complex 122
Skeleton of a triangulation 78
Skeleton of a triangulation, isomorphism of 79
Skeleton of a triangulation, unrestricted 121
Skeleton, complex 78 120
Space of continuous mappings 31
Space of countable weight 7
Space with countable basis 7
Space, compact Hausdorff 17
Space, compact metrizable 17
Space, compact topological 17
Space, complete metric 29
Space, connected 13
Space, decomposition 19
Space, discrete 16 28
Space, Euclidean 8
Space, Hausdorff 16
Space, Hilbert 9 171
Space, locally commected 41
Space, locally compact 24
Space, metric 7
Space, metrizable 10
Space, normal 16
Space, projective 22
Space, topological 4
Space, totally bounded metric 30
Special covering 189
Spectral theory xiv
Sperner’s lemma 156 160
Sphere with p cross-caps 109
Sphere with p handles 109
Sphere, closed solid 8
Spherical neighborhood 8
Star 27 72
Star in a partially ordered set 27
Star of a subcomplex 72 126
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