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Dugunji J. — Topology
Dugunji J. — Topology

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Название: Topology

Автор: Dugunji J.

Аннотация:

In this book, my aim is to provide the reader with a foundation in general topology that will adequately prepare him for further work in a broad variety of mathematical disciplines. The arrangement of the material is such that the book can also serve as a reference for the more advanced mathematician.
The reader is assumed to have a background of at least one semester of rigorous analysis; for such persons, the treatment herein is self-contained and the material can easily be covered in a two-semester course.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 447

Добавлена в каталог: 09.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{\infty}(I)$      301
$F_{\sigma}$-set      74
$l^2(\mathcal{A})$      191
$T_0$-space      138
$T_1$-space      138 156
$T_2$-space      138
$T_3$-space      141
$T_4$-space      144
$\bar{C}(Y;c)$      278
$\sigma$-compact space      240
$\sigma$-ring      76
Absolute neighborhood, retract      152
Absolute retract      151
Abstract simplicial complex      171
Accessible point      362
Accumulation point of filterbase      212
Accumulation point of net      210
Accumulation point of sequence      209
Adams, J.F.      383 407
Adherent point      69
Adjoin last element      31
Admissible topology      274
Affine space      416 ff.
Affine space of type m      187 417
AHEP      326
Alexander, J.W.      321 358
Alexandroff, P.      246
Algebra, boolean      6
Algebra, generated      281
Algebra, in $\bar{C}(Y;c)$      279
Algebra, unitary      279
Algebraic invariant      367
Analytic function      301
Anderson, R.D.      192
ANR (normal)      152 158 333
Antipodal (antipodal-preserving) map      347
AR (normal)      151 158 333
Arens, R.      214 229 260
Arhangel’skii, A.      169 196
Arzela — Ascoli theorem      267 276
Associate of a map      261
Attaching      127 ff
Attaching map      127 262
Attaching of spaces      127 135 145
Axioms of set theory      18 ff.
Baire metric      294
Baire space      249
Baire, R.      250 299
Ball of radius r      182
Banach space      415
Banach, S.      60 305
Barycentric coordinates      171
Barycentric mapping      172
Barycentric refinement      167 173
Barycentric subdivision      418
Base space, of fibering      392
Base, for uniform structure      201
Basis, for topology      64 67
Bernstein-Schroeder theorem      47 112 118
Binary relation      14 ff.
Binary relation, composition of      201
Bivalent set      92
Bolzano — Weierstrass property      229
Boolean algebra      6
Boolean ring      6
Borel family      56 61
Borel sets      76
Borsuk map      357
Borsuk, K.      346
Borsuk’s antipodal theorem      347 354
Borsuk’s separation theorem      357
Boundary      71
Boundary operator      74
Bounded metric      185
Bounded set      185
Brouwer domain-invariance theorem      358
Brouwer fixed-point theorem      341 353
Brouwer, L.E.J.      340 343
Brown, M.      157 358
Bruns, G.      213
C(Y)      284
C(Y;c)      284
c-topology      257
Canonical homeomorphism, in fiber structures      409
Canonical map, in direct spectra      421
Canonical map, in inverse spectra      428
Cantor diagonal process      231
Cantor set      22 104 112
Cantor, G.      296
Cardinal arithmetic      49 ff.
Cardinal, inaccessible      49
Cardinal, number      46
Cardinal, transfinite      47
Cardinals, class of      48
Carrier      332
Cartesian product topology      98 106
Cartesian product: family of sets      22
Cartesian product: family of spaces      98
Cartesian product: two sets      7
Category, first      250
Category, second      250
Cauchy filterbase      296
Cauchy sequence      292
Cech, E.      243
Cells, of polytope      418
Chain      30
Chain, maximal      58
Characteristic function of set      46
Characteristic of vector field on sphere      342
Choice function      23
Choice, axiom of      21 23 25 31 49 58
class      18
Class-formation, axiom of      18
Closed map      86
Closed operator      74
Closed relation      126
Closed set      68
Closure      69
Cluster point      70
Cofinal      424
Cohen, D.E.      248
Cohen, P.J.      21 49
Compact Hausdorff topology      226
Compact space      222 ff.
Compact, countably      228
Compact, locally      237
Compact, metric space      233
Compact, pseudo      231
Compact, relatively      237
Compact-open topology      257
Compact-open topology, metrization of      272
Compactification      242
Compactification, one-point      246
Compactification, Stone — Cech      243
Complement      5
Complete gauge space      309
Complete gauge structure      309
Complete metric      293
Complete metric space      294
Complete subspaces      308
Complete system of neighborhoods      63
Complete, topologically      294
Completely normal space      146
Completely regular space      153 159 200 208
Completion of gauge space      310
Completion of metric space      304 313
Complex, abstract simplicial      171
Complex, geometric realization of      172
Complex, vertex scheme of      172
Component      111
Component, path-      115
Component, quasi-      118
Composition, in H-structures      379 389
Composition, of maps      12
Composition, of relations      28 201
Condensation point      179
Cone      126
Cone over sphere      227
Conjoining topology      274
Connected      107 117 124
Connected, locally      113 125
Connected, path      114
Constant map      11
Constant path      376
Continuous at a point      80
Continuous convergence      268
Continuous in each variable separately      256
Continuous map      79
Continuous map into euclidean line      84
Continuous uniformly      234
Continuum Hypothesis      49
Contractible space      316
Convergence, in compact-open topology      267
Convergence, pointwise      272
Convergence, uniform      271
Convergence, uniform on compact sets      267
Convergent filterbase      212
Convergent net      210
Convergent sequence      209
Convex closure      415
Convex hull      411
Convex set      411
Coordinate function, in cartesian products      101
Coordinates of point      22
Countability, first axiom of      186
Countability, second axiom of      173
Countable basis at a point      186
Countable compactness      228
Countable connected Hausdorff space      157
Countable set      47
Countably paracompact      178
Covering      13
Covering homotopy      393
Covering homotopy, stationary      393
Covering map      393
Covering, closed      162
Covering, irreducible      160
Covering, neighborhood-finite      81
Covering, open      162
Covering, point-finite      152
Covering, star-finite      177
Cozero-set      400
Cube, Hilbert      192
Curtis, M.L.      396
Curve      105
Curve, spacefilling      105
De Morgan rules      5 9
Decomposition space, of map      129
Deformation retract      324 325 330
Deformation, of one set into another      324
Degree of map (of sphere in itself)      339
Dense      72
Dense, nowhere      92 250
Derived homotopy type      388
Derived set      70
Derived set operator      73
Diagonal      14
Diagonal enumeration      60
Diagonal process of Cantor      231
Diameter      185
Dieudonne, J.      131
Difference of sets      5
Direct limit map      423
Direct limit space      421
Direct limit space, generalized      426
Direct spectrum      420
Direct spectrum, generalized      426
Directed set      210
Discrete subspace      78
Discrete topology      63
Disjoint      3
Dispersion point      156
Distance      181
Distance between sets      185
Distance, Hausdorff      205 253
Domain invariance      358
Domination      374
Dowker, C.H.      132 136 170 416
Dual ideal      213
Dugundji, J.      188 229 419
Ecart      182 198
Eckmann, B.      407
Eilenberg, S.      361 374
Embedding map      89
Equiconnected      334
Equiconnected, locally      334 405
Equicontinuous      266
Equipotence class      45
Equipotent      45
Equivalence class      15
Equivalence relation      15 16
Equivalence, homotopy      366
Equivalence, pair homotopy      368
Equivalent basis      68
Equivalent metric      184
Equivalent uniformity      201
Euclidean line      63
Euclidean n-space      64
Evaluation map      260
Evaluation map, continuity of      274
Extended lifting function      397
Extended real line      77 85
Extension by continuity      216 218
Extension of function      13
Extension of uniformly continuous maps      302
Extension, Tietze Theorem      149
Exterior      92
Fadell, E.      398
Family of sets      8
Family of sets, lim inf and lim sup of      27
Family of sets, neighborhood-finite      81
Feldbau, J.      398
Fiber      392
Fiber space      393
Fiber structure      392
Fiber structure, cross section      393
Fiber structure, induced      395
Fiber-homotopic maps      398
Fiber-homotopy equivalence      398
Fiber-preserving map      398
Fibration      393
Fibration, Hurewicz      393
Fibration, local Hurewicz      403
Fibration, regular      393
Filter      213
Filterbase      211
Filterbase, Cauchy      296
Filterbase, determined by a net      211
Filterbase, maximal      218
Filterbase, neighborhood      211
Filterbase, subordinate      212
Finer topology      64
Finite character, property of      58
Finite intersection property      23
Finite set      2
Finite topology in vector space      131 133 416
Finitely additive measure      36
First axiom of countability      186
First category      250
First countable space      186
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