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Lefschetz S. — Algebraic topology
Lefschetz S. — Algebraic topology

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Название: Algebraic topology

Автор: Lefschetz S.

Аннотация:

When the present volume was first contemplated some five years ago it was primarily meant to be a second edition of the author's Topology A930, Volume XII of the American Mathematical Society Colloquium Series). It soon became evident however that the subject had moved too rapidly for a mere revised edition, and that a completely new book would have to be written. With the consent of the Colloquium Committee the task was undertaken by the author and resulted in the present work. Its basic topic, often referred to as "Combinatorial Topology," is in substance the theory of complexes and its applications.
Many factors have contributed to a great increase in the role of algebra in this subject. For this reason it is more appropriately described as "Algebraic Topology," and this explains the title of the volume.


Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1942

Количество страниц: 389

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^r$-concepts      330
$C^\omega$-concepts      331
$\Gamma$-complex      336
$\Gamma$-manifold      336
$\Gamma$-space      341
Acyclic      111 248
Addition of subsets in groups      41
Adherence      295
Aggregates, finite      13
Aggregates, infinite      13
Aggregates, locally finite      13
Aggregates, neighborhood-finite      13
Aggregates, point-finite      13
Alexander      41 88 124 127 173 174 181 189 204 227 228 244 255 282 285 304 309 310 315
Alexandroff      1 28 84 85 88 125 134 139 173 213 216 244 255 266 287 305
Analytical complex      333
Analytical manifold      331
Analytical spread      333
Analytical system of functions      330
Annihilator      60
annul      60
Antecedent of a singular complex      313
Antecedent of an Euclidean complex      97
Augmentation      130 221 248
Axioms, $T_0$, $T_1$, $T_2$, $T_i$      24
Axioms, first countability      6
Axioms, for metric spaces      33
Axioms, for topological spaces      5
Axioms, Hausdorff      24
Axioms, second countability      6
Axioms, triangle      33
Barycentric mapping and induced chain-mapping      291
Barycentric subdivision      169
Base      6
Base, at a point      6
Base, canonical      104
Base, closed      7
Base, countable      6
Base, equivalent      6
Base, of a group      50
Base, of a vector space      73
Basic class      29
Basic set      20
Begle      322 343
Betti group      102
Betti number      100 107 116 216 249
Bicompact      17
Borsuk      40 292
Boundary in a complex      89 90
Boundary of a chain      98
Boundary of a simplex      112
Boundary of a subset of a topological space      9
Bounded, totally      34
Bourbaki      19
Brouwer      196 299 304 305 321 342 343
Brown      333
Cairns      287 330 333 335
Carrier in a topological space      255
Carrier of a chain-mapping      152
Carrier of intersections in a complex      179
Cartan      285 335 340
Cech      1 79 128 173 189 213 216 244 252 254 273 285 342 343
cell      11
Cell, continuous      308
Cell, oriented      305
Cell, parametric      331
Cell, singular      311
Cell, singular oriented      312
Chain      15 48 98 113 229 271 282 312
Chain-deformation      152 160 242 313
Chain-derivation      165 313
Chain-derivation, reciprocal of      166
Chain-graph      149
Chain-homomorphism      48 242
Chain-homotopy      152 160 242 313
Chain-homotopy, prismatic      155
Chain-mapping      145 159 242 313
Chain-retraction      154 242
Chain-subdivision      163
Chain-subdivision, reciprocal of      163
Chain-transformation      145 159
CHARACTER      63 80
Character, group      63
Character, space      80
Characteristic number      94
Chevalley      41 73 213 244
Circuit      114
Circuit, absolute      114
Circuit, invariance under derivation      167
Circuit, modular or relative      115
Circuit, non-orientable      115
Circuit, orientable      115
Circuit, simple      115
Circuit, simplicial      115
Circuit, topological invariance      301
class      see Homology class
Class, intersection      181 207 220
Class, Kronecker index      120 181 207 220
Closure in a complex      89
Closure in a space      9
Coboundary      116
Cochain      116 229 283
Cocyle      116 216 229 242 271 283
Cofinal      5
Cohomology      116
Cohomology ring      181
Coincidences      191 210 318 324
Coinitial      5
Combinatorial cycles, classes, etc,      293
Compact spaces      17 18
Compact spaces, countably      17
Compact spaces, linearly      78
Compact spaces, locally      22
Compact spaces, locally linearly      79
Compact spaces, product of      10
Compact spaces, sequentially      38
Compacting      20
Compactum      17 37
Complement in a set      1
Complete metric space      35
Complexes      89
Complexes, $C^r$, analytic differentiable      333
Complexes, augmentable      130
Complexes, augmented      130
Complexes, closure-finite      91
Complexes, complete Vietoris      271
Complexes, continuous      308
Complexes, derived      164 167
Complexes, dual      91 93
Complexes, Euclidean      96
Complexes, infinite      127 232
Complexes, locally finite      91
Complexes, metric      239
Complexes, nomenclature of      341
Complexes, polyhedral      93
Complexes, reciprocal      197
Complexes, simple      132
Complexes, simplicial      92
Complexes, singular      312
Complexes, star-finite      91
Complexes, topological      327
Complexes, Vietoris      271
Component      see connectedness
Conet      214
Connectedness      14 90 110 217 257
Continuous transformation      7
Convention for vector spaces      72
Convergence      25
Convergence of cycles      263
Coset      45
Covering      13
Covering, closed      13
Covering, irreducible      247
Covering, open      13
Covering, shrinkable      26
Covering, strongly irreducible      247
Cycles      99 215 229 240 271 282
Cycles, absolute      113
Cycles, around a set      263
Cycles, relative or modular      113
Cycles, through a set      262
Cyclic      111 248
de Rham      204 285
Deformation      39
Deformation, cell      308
Deformation, theorem of Alexander — Veblen      309
Degree of a mapping      321
Dense      9
Dense, $\varepsilon$-dense      37
Derivation      164
Derived complexes      164 167
Derived complexes, barycentric      170
Diameter      34 239
Difference in groups      41
Difference of sets      1
Differentiable      330
DIMENSION      14 74 89 299 300
Direct system of groups      57 75
Directed system of sets      4
Discrete topology      8
Dissection of a complex      112
Dissection of a net      223
Dissection of a space      248
Distance      33
Division-closure group      68
Dowker      252
Dual categories      121
Dual complex      91 93
Dual pairing      66 81
Dual systems      67
Dual weakly dual systems      83
Duality theorems for combinatorial manifolds      202
Duality theorems for geometric manifolds      303 304
Duality theorems for groups      66 81
Duality theorems for nets      218 224 227 230 233
Duality theorems for topological spaces      248 250 255
Duality theorems for webs      236
Duality theorems, absolute      117 121 129 219 230 233 248 303
Duality theorems, of Alexander type      124 129 204 227 256 304
Duality theorems, of Poincare      203
Duality theorems, relative      122 203 224 248
e aggregates, etc,      34 37 39
Eilenberg      128 311
Essential cycle      216
Essential element      79
Euler characteristic      104
Euler — Poincare' formula      104
Extension of continuous functions      28
Extension of fields      85
Extension of transformations      2
Extension theorem of Tietze      28
f-, fi-chain-mapping      159
Face      90
Factor-group      45
Field      72
Field, character      80
Field, extension      85
Finite intersection property      17
Fixed elements of a chain-mapping      191
Fixed point      318 324
Fixed point, property      326
Flexner      174 188 342
Free group      50
Freudenthal      41 181 213
Function      2
Function, locally finite      283
Fundamental group      310
Fundamental group, zero-cocycle      131 221
Generators of a group      49
Geometrical elements      293
Gordon      174 181
Graph      2 4
Graph of a chain-mapping      149
Graph of multiplication in a complex      175
Grating      279
Grating, spectrum      279
Group      41 47.
Group, manifold      335
Group, multiplication      59
Group, space      336
H-net, H-conet      235
Hausdorff      258
Hausdorff space      6 24
Hausdorff — Lennes separation condition      15
Heegaard      335
Hilbert parallelotope      12
HLC* space      322
Hodge      286 287
Homeomorphism      7
Homology      98
Homology, class      99
Homology, group      99
Homology, group of product of compact Hausdorff spaces      265
Homology, group of product of complexes      139
Homology, group of product of nets      222
Homology, ring      207
Homomorphism      44
Homomorphism, in the algebraic sense      44
Homomorphism, linear      72
Homotopy      39
Homotopy, operator      152
Hopf      28 88 134 139 266 287 335 337 340
Hurewicz      300 311 336
i-chain-mapping      159
Ideal elements      234
Identification      3
Identification, topological      12
Imbedding      3
Imbedding, topological      13
Incidence matrices      101
Incidence numbers      89 92 95 97 312 327 329
INDEX      see Kronecker index
Indexed system      3
Indicatrix      305
Induced chain-mappings      162 185
Injection      48 57 113 225 234 251
Interior      8
Interior, point      9
Intersections and chain-mappings      184
Intersections and subdivision      186
Intersections in a product of combinatorial manifolds      208
Intersections in a product of complexes      187
Intersections in combinatorial manifolds      206
Intersections in complexes      178
Intersections in differentiate manifolds      834
Intersections in infinite complexes      188
Intersections in nets      218 224
Intersections in sets      1
Intersections in simplicial complexes      188 189
Intersections in topological spaces      255
Intersections of singular elements in a geometric manifold      316
Intersections, carriers of      179 255
Intersections, components of      178
Intersections, induced      184
Intersections, topological invariance of      294 305
interval      8
Invariant factors      51
Inverse mapping sequence of spaces      33
Inverse system of groups      54
Inverse system of spaces      31
1 2 3
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