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Fritsch R., Piccinini R. — Cellular Structures in Topology (Cambridge Studies in Advanced Mathematics 19)
Fritsch R., Piccinini R. — Cellular Structures in Topology (Cambridge Studies in Advanced Mathematics 19)

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Название: Cellular Structures in Topology (Cambridge Studies in Advanced Mathematics 19)

Авторы: Fritsch R., Piccinini R.

Аннотация:

This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 336

Добавлена в каталог: 22.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\bar{f}$-collar      20
(Geometric) standard n-simplex      93
2-category      133
Absolute neighbourhood retract (ANR)      281
Acyclic fibration      178
Acyclic models      286
Adams, J.F. (1930-1989)      88
Addition law (L3)      263
Adjoint (of a simplicial map)      157
Adjoint functor generating principle      303
Adjunction of n-cells      12
Adjunction space      258
Admissible pair (of maps)      292
Affine embedding      91
Affinely independent      89
Alder, M.D.      127
Alexander, J.W. (1888-1971)      131
Alexandroff, P.S. (1896-1983)      131
Allaud, G.      272
Anodyne extension      172
Approximation      68
Associated simplicial set (to an ordered simplicial complex)      152
Attaching (simplicial)      144
Attaching map      12 259
Attaching space      258
Axiom of Choice      31
Axiom of Countable Choice      31
Axiom of multiple choice      31
Ball      1
Barratt, M.      131 222
Barycentre      92
Barycentric coordinates      90
Barycentric refinement of a covering      248
Barycentric subdivision      111
Base (of a euclidean cone)      92
Base (of a Kan fibration)      171
Base space (of a fibration)      255
Based homotopy      286
Based map      286
Borges, C.R.      33 304 305
Borovikov, V.      131
Borsuk, K. (1905-1982)      282 283
Boundary (of standard p-simplex)      142
Bouquet of spheres      18
Bourbaki, N.      252 303
Brouwer theorem      300 302
Brown, R.      54 88 242 251 252 259 266 271 279 298 299
Canonical CW-structure of a ball      24
Canonical simplicial map      200
Cantor set (middle third set)      224 252
Carrier      23 90 98 112
Cartesian product      241
Category of finite ordinals      132
Category of n-ads with type of CW-n-ads $TCW^{n}$      230
Category of presimplicial sets PSiSets      165
Category of simplices functor      141
Category of simplicial sets SiSets      139
Category of small categories      141
Category of spaces with type of CW-complexes TCW      223
Category of topological spaces Top      241
Category of weak Hausdorff k-spaces wHk(Top)      243
Cauty, R.      33
Ceder, J.G.      250
Cell (closed, open, regular)      11
Cell complex      51
Cell path-connected      41
Cell subcomplex      51
Cellular approximation theorem      73
Cellular map      56
Cellular map of (relative) CW-complexes      56
Cellular partial map      62
Chain complex functor      284
Characteristic map      12 259
Classifying set      192
Closed cofibration      251
Closed n-cell      11
Closed regular n-cell      11
Closure finite      40 52
Cogluing theorem      270
Collar      20
Collaring      19
Columbus, G. (1451-1506)      2
Compact-open topology      241
Compactly closed      242
Compatible sequence of maps      273
Complementary face      89
Complete weak homotopy equivalence      231
Composable (pair)      139
Cone      269
Cone (Euclidean)      92
Cone (of a presimplicial set)      167
Cone functor (of presimplicial sets)      167
Connected simplicial set      194
Convenient      242
Convex covering      118
Convexely independent subfamily      95
Coproducts of CW-complexes      57
Coreflective subcategory      152
Cosimplicial map      146
Cosimplicial object (in a category)      138
Cosimplicial set      146
Countable CW-complex      40
Countable family      248
Countable simplicial complex      121
Covering      248
Covering dimension      299
Covering projection      256
Covering space      256
Covering transformation      291
Cross-section      270
cube      96
Curtis, E.B.      220
CW-complex      22
CW-complex of finite dimension      46
CW-complex of finite type      40
CW-n-ad      230
CW-structure      22
Degeneracy operator      135
Degenerate simplex      144
Degree      90
Determined (by a family of subspaces)      246
Diameter (of a geometric simplex)      91
Dimension (of a CW-complex)      46
Dimension (of a Euclidean complex)      100
Dimension (of a minimal pair)      149
Dimension (of a simplex)      139
Dimension (of a simplicial set)      146
Dimension (of an operator)      132
Dimension and embedding      46
Directly equivalent pairs      149
Dold, A.      131 272
Domination      288
Dowker, C.H. (1912-1982)      87 131
Dugundji extension theorem      281
Dugundji, J. (1919-1965)      54 242 248 249 253 302
Dunce hat      152
Dydack, J.      225 239
Dyer, E.      55 267
Eckmann, B.      292
EDGE      89
Eggs of Columbus      2
Eilenberg — MacLane spaces      87 193
Eilenberg — Zilber lemma      145
Eilenberg — Zilber property      149
Eilenberg, S.      55 87 131 197 220 221 267 285 286
ELCX-n-ad      232
ELCX-space      118
ELCX-subspace      119
Elementary degeneracy operator      135
Elementary expansion      65
Elementary face operator      133
Engelking, R.      54 299 300 302
Equi locally convex space (ELCX-space)      118
Equi locally convex structure (ELCX-structure)      118
Equi locally convex subspace (ELCX-subspace)      119
Equiconnecting homotopy      118
Euclidean complex      97
Euclidean realization of a simplicial complex      122
Evaluation map      241
Expanding sequence      273
Exponential law      243
Extension functor      212
Face (of a simplex)      89 110
Face operator      133
Fat realization      166
Fibration      171 254
Fibre      143
Fibre (of a fibration)      255
Fibre homotopic (simplices are-)      181
Fibre homotopy      255
Fibre homotopy (of simplices)      181
Fibre homotopy equivalence      255
Fibre map      255
Figure-eight      287
Filling of horns      171
Filtration (of a space)      22
Final topology      246
Finite CW-complex      40
Finite dimensional CW-complex      46
Finite dimensional simplicial complex      121
Finite euclidean complex      97
Finite ordinals (category)      132
Finite presentation (of groups)      81
Finite simplicial complex      121
Finite type (CW-complexes)      40
Finney, R.L.      127
Folklore, J.      54
Forgetting degeneracies      165
Fox, R.H. (1913-1973)      131
Frechet space      26 27 55
Freudenthal, H.      54
Freyd, P.      221
Fritsch, R.      197 198 221 222
Function n-ad      234
Fundamental group      287
Fundamental group of a CW-complex      78
Fundamental groupoid      298
Gabriel, P.      198 220 221 222 247 284 285 304
Gale, D.      242
Generator (of a simplicial set)      144
Geoghegan, R.      225 239
Geometric realization      112 139
Geometric realization (of a simplicial map)      121 140
Geometric realization functor      121 140 153
Giever, J.B.      221
Global set (of a Euclidean cone)      92
Gluing theorem      266
Groupoid      298
Gugenheim, V.      220
Hanai, S.      27
Hanner, O.      131
Hauptvermutung      112 131
Heath, P.R.      271 304
Hilbert cube      48 302
Hilton, P.J.      170 283 290 291 292
Homology      284
Homology functor      284
Homotopy addition theorem      297
Homotopy equivalence of pairs      278
Homotopy extension property      250
Homotopy groups      287
Homotopy groups of maps      292
Homotopy lifting property      254
Homotopy sequence of a fibration      297
Homotopy sequence of maps      293
Homotopy type      266
Horizontal composition law (L1)      262
Horn      170
Hu, S.      54
Hurewicz fibration      185 255
Hurewicz, W. (1904-1957)      301
Hyman, D.M.      54
Identity operators      133
Increasing the connectivity of maps      83
Induced      142 143
Infinite ball      2
Infinite collar      27
Infinite projective space      25
Infinite simplex      114
Infinite sphere      2
Initial topology      248
Interior (of a simplex)      89
Invariance of domain (theorem)      302
inversion      6
Isomorphic simplicial complexes      111
k-horn      170
k-ification      242
k-simplex      89 110
k-space      242
Kamps, H.      271 287
Kan condition      221
Kan fibration      171
Kan set      172
Kan, D.M.      197 198 220 221 222 303
Kaplan, S.      249
Kelley, J.L.      i 245
Kodama, Y.      221
Kolmogorov, A.N. (1903-1989?)      131
Kuratowski — Wojdyslawski embedding theorem      281
Lamotke, K.      197 220 221 222 284
Latch, D.M.      197 221
LEC-spaces      253
Lefschetz, S. (1884-1972)      i
Lens space      169 170
Lewis, L.G., jr      266
Lifting property      254
Lifting theorem      291
Lillig, J.      252
Lindeloef space      50
Link      101
Local vertex ordering      111
Locally contractible space      28
Locally equiconnected spaces (LEC)      253
Locally finite CW-complexes      40
Locally finite family      248
Locally finite partition of unity      249
Locally finite simplicial, complex      121
Locally path-connected      29
Locally trivial map      163 271
Locally trivial simplicial map      143
Loop space      256
Lundell, A.T.      51 55 62 131
m-connected map      295
M-equivalence      295
MacLane, S.      i 87 287 220 283
Map (simplicial) induced from      143
Map induced from      258
Mapping cone      269
Mapping cylinder      264
Mapping space      241
Mapping track      270
Mardesic, S.      281
Massey, W.S.      88 299
Mather, M.R.      131
May, J.P.      220
McCord, M.C.      244 247
Menger — Noebeling theorem      302
Menger, K. (1902-1985)      302
Metric topology      113
Metzler, W.      131
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