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| Lefschetz S. — Introduction to topology |
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| Предметный указатель |
Isomorphic simplicial complexes 88—89
Isomorphism in groups 38
Isomorphism of simplicial complexes 88—89
Isomorphism, linear 39—40
Join 94
Join, closed 94
Jordan curve 30
Jordan curve, exterior (points) of 61
Jordan curve, interior (points) of 61
Jordan curve, one-sided 80
Jordan curve, two-sided 80
Jordan — Brouwer theorem 84
Jordan — Schonflies theorem 62
Jordan-curve theorem 61
Kernel of homomorphism 38
Klein bottle 108
Kronecker index of zero-chains 92
Last vertex 113
Lebesgue number 37
Lefschetz duality theorem for relative manifolds 203
Lense-space 7 182
Lindelof theorem 31
Linear chain operator reduced modulo a subcomplex 88—89
Linear graph 47
Linear isomorphism 39—40
Linear transformation of complexes 52—53
Linear transformation of simplicial complexes 55
Linear transformation of vector spaces 39—40
Linearly dependent elements of a vector space 39
Linearly independent, cycles (with respect to homology) 95
Linearly independent, elements of a vector space 39
Linearly independent, points (in an Euclidean space) 95
Linked complex (of a simplex) 186
Local Group 207
Locally finite covering 184
Locally topological mapping 169
Manifolds with regular boundary 203—204
Manifolds, absolute 202
Manifolds, combinatorial 193
Manifolds, combinatorial absolute 2-dimensional 73
Manifolds, differentiate 184
Manifolds, doubly covering 188
Manifolds, identical 184
Manifolds, n-dimensional 183
Manifolds, open 202
Manifolds, orientable 187
Manifolds, oriented 187
Manifolds, Poincare n- 186
Manifolds, relative 202
Manifolds, topological 183
Mappings 33
Mappings, barycentric 120
Mappings, chain, homotopic 144
Mappings, chain, in a common carrier 146
Mappings, chain- 52—53
Mappings, continuous 33
Mappings, essential 43
Mappings, homotopic 42 170
Mappings, inessential 43 131
Mappings, locally topological 169
Mappings, onto 26
Mappings, radial 130—131
Mappings, regular, sense-preserving 127
Mappings, sense-reversing 127
Mappings, univalent 26
mesh 29
Metric spaces 28—29
Metrics, equivalent 31
Metrizable 31
Mobius strip 79
Negatively related 88
Neighborhood 32
Nerve 180
Nested segments 28
Non-concordantly oriented geometric simplexes 96
Non-orientable (surface) symbols 75—76 78
Non-orientable circuit 78
Normal, covering pair 199
Normal, forms for the orientable and non-orientable surface symbols 78—79
Normal, subcomplex 199
One-one transformation 26
Onto transformation 26
Open of the reciprocal complex 202
Open, covering 34
Open, manifold 202
Open, n-cell 30
Open, polyhedron 198
Open, set 30
Open, subcomplex 196
Order of a point with respect to a Jordan curve 125
Orientable (surface) symbols 75—76
Orientable circuit 106
Orientable manifold 187
Orientable manifold with regular boundary 203—204
Orientation 87
Orientation by propagation 106
Orientation, -function 88
Oriented geometric simplexes 96
Oriented, geometric simplexes, concordantly 96
Oriented, geometric simplexes, manifolds 187
Oriented, geometric simplexes, non-concordantly 96
Oriented, simplicial complexes 88
Orienting a p-simplex 87
Over 169
p-cyclic 23
p-section of a complex 88
Parallelotope 36
Parallelotope, Hilbert 43—44
Parameters for a manifold 183—184
Parametric covering 184
Parametric n-cell 183—184
Path 158
Path of a point in a homotopy 42
Path, closed 158
Path, end points of 158
Path, initial point of 158
Path, inverse 158
Path, terminal point of 158
Paths, homotopic 159
Paths, product of 159
Poincare duality theorem 188
Poincare manifold 186
Point of condensation 36
Point over its projection 169
Polyhedron 47
Polyhedron, closed 198
Polyhedron, covered by a complex 47
Polyhedron, open 198
Polyhedron, simplicial 97
Polyhedron, triangulated into a complex 47
Positively related 88
Principle of relatiyization 33
Prismatically related chain-mappings 146
Problem of the seven bridges of Konisberg 84
Product of (topological) spaces 40
Product of groups 40
Product of paths 159
Product of sets 40
Product of vector spaces 40
Product, topological 40
Projection of a group into a factor-group 38
Projection of the universal covering space of a polyhedron into the polyhedron 169
Projective plane 83
Proper face 46
Punctured oriented n-sphere 170
Reciprocal complex 188 192
Reciprocal of a chain-mapping 206—207
Reciprocal of a complex 188 192
Reciprocal of a subcollection of simplexes of a complex 192
Refine 34
| refinement 122
Refinement of complexes 122
Refinement of coverings 34
Region 30
Region, spherical 29
Regular, boundary 203—204
Regular, homotopy 130—131
Regular, mappings 130—131
Regular, set of real functions 183
Regularly imbedded 184
Relative circuit 197
Relative, circuit, mod a subcomplex 197
Relative, cycle 196
Relative, homology theory 193
Relative, manifold 202
Relatively, closed sets 33
Relatively, open sets 33
Relatiyization principle 33
Reoriented simplicial complexes 88
Representative of a homology class 201
Ring surface 109
Schonfiies theorem 62
segments 28
Segments, nested 28
Sense-preserving homeomorphism 127
Sense-preserving mappings 127
Sense-reversing mappings 127
Separable pairs of symbols 77
Separable space 31
Set-transformation 110
Set-transformation, closed 110
Set-transformation, simplicial 112
Set-transformation, zero-cyclic 146
Sets 26
Sets, closed 32
Sets, connected 33
Sets, convex 37
Sets, disjoint 27
Sets, Euclidean 28
Sets, null 26
Sets, open 30
Sets, relatively closed 33
Sets, relatively open 33
Significant part of a mapping of n-spheres 132
Simple n-circuit 105
Simplexes 45 87
Simplexes in a chain 60
Simplexes, closed 96
Simplexes, connected collection of 105
Simplexes, degenerate 90
Simplexes, geometric 96—96
Simplexes, linked complexes of 186
Simplexes, p-dimensional 87
Simplicial 54—55
Simplicial, chain mappings, carriers of 112
Simplicial, chain-mappings 54—55 112
Simplicial, complexes 88
Simplicial, complexes, isomorphic 88—89
Simplicial, complexes, oriented 88
Simplicial, complexes, reoriented 89
Simplicial, complexes, topological 98
Simplicial, linear transformations 54—55
Simplicial, polyhedron 97
Simplicial, set transformations 112
Simply connected spaces 162
Single-valued functions and transformations 26
Singular points, complex (of an algebraic curve) 206
Singular points, real 206
Singular points, solid n-sphere 30
Spaces,  43
Spaces, compact 35
Spaces, connected 33
Spaces, discrete 31
Spaces, Euclidean 28
Spaces, Hausdorff 31
Spaces, Hilbert 43—44
Spaces, lense- 43—44
Spaces, metric 28—29
Spaces, separable 31
Spaces, simply connected 162
Spaces, topological 30
Spaces, universal covering 169
Spaces, vector 38
Spenner lemma 117
Spheres (topological) 30
Spheres (topological), punctured oriented 170
Spherical regions 29
Spheroids 29
Star (of a simplex) 55 89
Star-projection 56 121
Star-related 121
Star-set 55 120
Subcell 184
Subcomplex 47
Subcomplex, closed 196
Subcomplex, closed, of the reciprocal complex 202
Subcomplex, open 196
Subcomplex, open, of the reciprocal complex 202
Subdivided arc 52
Subdivided chain 53
Subdivided circumference 51
Subdivision 49 113
Subdivision of a polyhedron 42
Subdivision, -chain 53
Subdivision, barycentric 113
Subdivision, elementary 49
Subgroup 38
Subpath of a complex 159
Subpolyhedron 198
Subset 26
Subspace (of a vector space) 40
Supremum 27
Surface symbols 75—76
Surface symbols, non-orientable 78
Surface symbols, orientable 78
Surfaces (closed) 72
Surfaces (closed), equivalent 77
Terminal point of a path 158
Tetrahedron boundary 52
Topological manifolds 183
Topological mappings, locally 169
Topological product (spaces) 40
Topological simplicial complexes 98
Topological spaces 30
Topological spheres 30
Topological transformations 29 33
Topologized 30
topology 29 30 32
Topology, discrete 31
Trace (invariant of a chain-mapping) 154
Transformations 26
Transformations of coordinates, direct and inverse 96
Transformations,  - 34
Transformations, continuous 33
Transformations, into 26
Transformations, inverse 26
Transformations, linear 39—40
Transformations, one-one 26
Transformations, onto 26
Transformations, topological 29 33
TREE 105
Triangle axiom 28
Triangulation of a polyhedron 47
Union (of sets) 26—27
Univalent mappings 26
Universal covering space, of a polyhedron 169
Vector spaces 38
Vector spaces, base of 39
Vector spaces, dimension of 39
Vector spaces, direct sum of 40
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