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Lefschetz S. — Introduction to Topology
Lefschetz S. — Introduction to Topology

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Название: Introduction to Topology

Автор: Lefschetz S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 223

Добавлена в каталог: 14.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$p$-section of a complex      88
$T_{1}$-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, $\epsilon$-      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, countable      31
Base, of a topological space      31
Base, of a vector space      39
Betti numbers      68
Betti numbers, bicontinuous functions      29
Betti numbers, border      55—56 121 122
Betti numbers, bound      50 196
Betti numbers, of a complex      93
Betti numbers, of a polyhedron      151
Boundary, chains      91
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, 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, $n$-      30
Cell, closed      30
Cell, open      30
Cell, parametric      184—185
Chain, integral $p$-      89
Chain, mod two      50
Chain-boundary      50
Chain-derivation      116
Chain-derivation, inverse of      116
Chain-mapping      52—3
Chain-mapping, reciprocal of      206—207
Chain-mapping, simplicial      54—5 112
Chain-mappings      52—3
Chain-mappings, homotopic      144
Chain-mappings, prismatically related      146
Chain-subdivision      49
Characteristic (of a complex)      101
Characteristic (of a complex), Euler — Poincar$\acute{e}$      69
Circuit      105
Circuit, $n$-      105
Circuit, absolute      197
Circuit, non-orientable      106—107
Circuit, orientable      106
Circuit, relative      197
Circuit, simple $n$-      105
Closed, $n$-cell      30
Closed, arc      34
Closed, covering      34
Closed, join      94
Closed, path      158
Closed, polyhedron      198
Closed, set      32
Closed, set-transformation      110
Closed, simplex      96
Closed, subcomplex      196
Closed, subcomplex of the reciprocal complex      192 202
Closed, surface      72—73
Closure, of a set      32
Closure, of a simplex      88
Closure, of a simplex of the reciprocal complex      192
Collection      26
Collection, $\epsilon$-      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, $n$-(dimensional)      45 47
Complex, $p$-section of      88
Complex, connected      104
Complex, derived      112—113
Complex, generalized      140
Complex, geometric      97
Complex, linked      186
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, $\epsilon$-      34
Covering, closed      34
Covering, locally finite      184
Covering, open      34
Covering, parametric      184
Cycle (of a complex)      51 91
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), of a complex mod a subcomplex      196
Cycle (of a complex), relative      196
Cycles, linearly independent (with respect to homology)      91
Cyclic, $p$-      93
Cyclic, in the dimension $p$      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—13
Derivation, chain      116
Derived, $n$-th      112—13
Derived, (first)      112—13
Derived, barycentric      113
Diameter      29
Differentiable 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, axioms      28
Distance, between sets      29
Distance, Euclidean      28
Distance, function      29
Doubly covering manifold      188
Duality theorems, -aggregate      29
Duality theorems, -collection      29
Duality theorems, -covering      34
Duality theorems, Alexander      205
Duality theorems, for manifolds with regular boundary      204
Duality theorems, Lefschetz, for relative manifolds      204
Duality theorems, Poincar$\acute{e}$      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, -one,$n$-dimensional      28
Euclidean, distance      28
Euclidean, set      28
Euclidean, space      28
Euclidean, sphere      30
Euler — Poincar$\acute{e}$, characteristic      101
Euler — Poincar$\acute{e}$, relation      69
Extension, barycentric (of a simplicial set-transformation)      120
Extension, of a mapping      26
Extension, of homotopy      61 131
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
Geometric, simplexes 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 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, $\check{C}$ech, 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, -$\epsilon$      42
Homotopy, of punctured oriented $n$-spheres      170
Homotopy, regular      130—131
Imbedded, regularly      184
Incidence matrices      99
Incidence numbers, of the reciprocal complex      191
Incident (with one another)      46 87
Index, Kronecker      70
Index, of a Jordan curve with respect to a vector field      125
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, function      26
Inverse, of chain derivation      116
Inverse, path      158
Inverse, transformation      26
Inverse, transformation of coordinates      96
Island      171
Isomorphic      27
Isomorphic, complexes      48
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