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Aleksandrov P.S. — Combinatorial topology. Volume 1
Aleksandrov P.S. — Combinatorial topology. Volume 1



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Название: Combinatorial topology. Volume 1

Автор: Aleksandrov P.S.

Аннотация:

Fundamental topological facts, together with detailed explanations of the necessary technical apparatus, constitute this clearly written, well-organized three-part text. Part 1 deals with certain classic problems without using the formal techniques of homology theory; parts 2 and 3 focus on the central concept of combinatorial topology, the Betti groups. Numerous detailed examples.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1956

Количество страниц: 237

Добавлена в каталог: 21.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-approximation, barycentric      177
$\epsilon$-covering      36
$\epsilon$-displaoement      171
$\epsilon$-mapping      170
$\epsilon$-neighborhood      8
$\epsilon$-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 $\leq r$, characterization of      18
Bicompacta of weight $\leq r$, 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 $B_{n}$      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
1 2 3
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