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| Lefschetz S. — Introduction to topology |
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| Предметный указатель |
 -space 43
Absolute, circuit 197
Absolute, cycle 196
Absolute, homology class 201
Absolute, homology group 200
Absolute, manifold 202
Acyclic 93
Acyclic in the dimension p 93
Aggregate,  - 29
Alexander duality theorem 204—205
Alexandroff mapping theorem 180—181
Algebraic curve 206
Algebraic curve, singular points of 206
Antipodal 135
Arc, closed 34
Arc, subdivided 52
Arcwise connectedness 62
Barycentric, coordinates 95
Barycentric, derived 113
Barycentric, extension (of a simplicial set-transformation) 120
Barycentric, mapping 120
Barycentric, subdivision 113
Base of a topological space 31
Base of a vector space 39
Base, countable 31
Betti numbers 68
Betti numbers of a complex 93
Betti numbers of a polyhedron 151
Betti numbers, bicontinuous functions 29
Betti numbers, border 55—56 121—122
Betti numbers, bound 50 196
Boundary of a chain 90
Boundary of a simplex 88
Boundary of a subset of a topological space 32
Boundary of the reciprocal complex 192
Boundary, chains 91
Boundary, regular 203—204
Boundary, tetrahedron 52
Bounding cycle 91
Brouwer degree of mappings 126—127
Brouwer fixed point theorem 117
Brouwer invariance of dimension theorem 207
Carrier of a simplicial chain-mapping 112
cell 30
Cell, closed 30
Cell, n- 30
Cell, open 30
Cell, parametric 184—185
Chain, integral p- 89
Chain, mod 2 50
Chain-boundary 50
Chain-derivation 116
Chain-derivation, inverse of 116
Chain-mapping 52—53
Chain-mapping, reciprocal of 206—207
Chain-mapping, simplicial 54—55 112
Chain-mappings 52—53
Chain-mappings, homotopic 144
Chain-mappings, prismatically related 146
Chain-subdivision 49
Characteristic (of a complex) 101
Characteristic (of a complex), Euler — Poincare 69
Circuit 105
Circuit, absolute 197
Circuit, n- 105
Circuit, non-orientable 106—107
Circuit, orientable 106
Circuit, relative 197
Circuit, simple n- 105
Closed arc 34
Closed covering 34
Closed join 94
Closed n-cell 30
Closed path 158
Closed polyhedron 198
Closed set 32
Closed set-transformation 110
Closed simplex 96
Closed subcomplex 196
Closed surface 72—73
Closedsubcomplex of the reciprocal complex 192 202
Closure of a set 32
Closure of a simplex 88
Closure of a simplex of the reciprocal complex 192
Collection 26
Collection, - 29
Combinatorial absolute 2-manifold 73
Combinatorial manifold 195
Commutator of a group 166
Compact space 35
Compactum 35
Complement of a set 27
COMPLEX 46
Complex, connected 104
Complex, derived 112—113
Complex, generalized 140
Complex, geometric 97
Complex, linked 186
Complex, n-(dimensional) 45 47
Complex, p-section of 88
Complex, reciprocal 192
Complex, simplicial 88
Complex, topological simplicial 98
Complexes, isomorphic 48
Components of a complex 104
Components of a space 34
Concentrating a mapping 133
Concordantly oriented 96
Condensation point 36
Cone 43
Conformal mapping theorem 62
Connected collection of simplexes 105
Connected complex 104
Connected set 33
Connected space 33
connecting 105
Continuity, metric 33
Continuity, topological 33
Continuous functions 29 33
Continuous mappings 33
Continuous transformations 33
Contractible 42
Convex set 37
Coordinates, direct transformation of 96
Coordinates, inverse transformation of 96
cosets 38
Countable base 31
Covering 34
Covering pair of a complex 199
Covering pair of a complex, normal 199
Covering, - 34
Covering, closed 34
Covering, locally finite 184
Covering, open 34
Covering, parametric 184
Cycle (of a complex) 51 91
Cycle (of a complex) of a complex mod a subcomplex 196
Cycle (of a complex), absolute 196 201
Cycle (of a complex), bounding 91
Cycle (of a complex), elementary 70 166
Cycle (of a complex), fundamental 107
Cycle (of a complex), integral p- 91
Cycle (of a complex), relative 196
Cycles, linearly independent (with respect to homology) 91
Cyclic in the dimension p 93
Cyclic, p- 93
Cylinder 41—42
Dedekind cut 27
Deformable into a point 42
Deformation 42 144
| Degenerate simplex 90
Degree of a mapping, Brouwer 124
Degree of regular mappings of disks 130
Degree of regular mappings of disks into spheres 131
Dense subsets 31
Derivation 112—113
Derivation, chain 116
Derived barycentric 113
Derived, (first) 112—113
Derived, n-th 112—13
Diameter 29
Differentiate manifold 184
Dimension of a complex 42
Dimension of a simplex 87
Dimension of a simplicial complex 88
Dimension of a vector space 39
Dimension of the reciprocal complex 123—124
Dimensional invariance theorem 207
Direct sum of vector spaces 40
Direct transformation of coordinates 96
Discrete space 31
Discrete topology 31
Disjoint sets 27
Disk 30
Distance 28
Distance between sets 29
Distance, axioms 28
Distance, Euclidean 28
Distance, function 29
Doubly covering manifold 188
Duality theorems for manifolds with regular boundary 204
Duality theorems, -aggregate 29
Duality theorems, -collection 29
Duality theorems, -covering 34
Duality theorems, Alexander 205
Duality theorems, Lefschetz, for relative manifolds 204
Duality theorems, Poincare 188
EDGE 96
Edge, -homotopy 42
Element 26
Elementary, cycle 70 166
Elementary, subdivision 49
End points of a path 158
Equivalent metrics 31
Essential mapping 43
Essential mapping, -transformation 29
Euclidean, -1,n-dimensional 28
Euclidean, distance 28
Euclidean, set 28
Euclidean, space 28
Euclidean, sphere 30
Euler — Poincare characteristic 101
Euler — Poincare relation 69
Extension of a mapping 26
Extension of homotopy 61 131
Extension, barycentric (of a simplicial set-transformation) 120
Exterior (points) of a Jordan curve 61
Face 46 87 96
Face of the reciprocal complex 191
Face, proper 87
Face, proper face of the reciprocal complex 191
Factor-groups 38
Field 38
Finite intersection property 34
First derived (= derived) 112—113
First vertex 113
Fixed point 117—118
Fixed point of a mapping of a polyhedron 155
Function 26
Function, bicontinuous 29
Function, continuous 29 33
Function, inverse 26
Function, single-valued 26
Fundamental cycle (of a simple n-circuit) 107
Fundamental group 161
Generalized complex 140
Genus 78
Geometric antecedent (of a complex) 48
Geometric complex 48 96—97
Geometric representation 49
Geometric simplexes 95—96
Geometric simplexes concordantly oriented 96
Geometricsimplexes non-concordantly oriented 96
Graph 47
Graph, linear 47
Group made commutative 166
groups 28
Groups, additive 28
Groups, commutative 28
Groups, factor 28
Groups, fundamental 161
Groups, homotopy 174
Groups, integral p-th homology 91
groups, local 207
Groups, multiplicative 28
Hausdorff space 31
Hilbert parallelotope 43—44
Hilbert parallelotope, space 43—44
Homeomorphism 29
Homeomorphism, sense-preserving 158
Homologous (to zero) modulo a subcomplex 196
Homology 91
Homology, class of a polyhedron 151
Homology, class, absolute 201
Homology, class, integral 91—92
Homology, group, absolute 200
Homology, group, integral p-th 91
Homology, theory, Cech, theory, relative 195
Homomorphism in groups 38
Homotopic chain-mappings 144
Homotopic chain-mappings in a common carrier 146
Homotopic mappings 42
Homotopic paths 159
Homotopic to a constant 42
Homotopy groups 174
Homotopy in mappings 42
Homotopy in mappings of punctured oriented n-spheres 170
Homotopy in mappings, - 42
Homotopy in mappings, regular 130—131
Imbedded, regularly 184
Incidence matrices 99
Incidence numbers, of the reciprocal complex 191
Incident (with one another) 46 87
Index of a Jordan curve with respect to a vector field 125
Index, Kronecker 70
Indicatrix 96
Inessential mapping 43 131
Infimum 27
Initial point of a path 158
Integral, p-chain 89
Integral, p-cycle 91
Integral, p-th homology classes 91—92
Integral, p-th homology group 91
Interior (points) 32
Interior (points) of a Jordan curve 61
Interlocking systems 58—59
Intersection in sets 27
interval 27
Into transformation 26
Invariance of dimension theorems, Brouwer 207
Invariance, dimensional 123—124
Inverse of chain derivation 116
Inverse, function 26
Inverse, path 158
Inverse, transformation 26
Inverse, transformation of coordinates 96
Island 171
Isomorphic 27
Isomorphic complexes 48
Isomorphic geometric complexes 97
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