Pears A.R. — Dimension theory of general spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Pears A.R. — Dimension theory of general spaces

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Название: Dimension theory of general spaces

Автор: Pears A.R.

Аннотация:

A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces. It makes the subject accessible to beginning graduate students and will also serve as a reference work for general topologists. Two introductory chapters summarize standard results in general topology, and cover material on paracompactness and metrization. The principal definitions of dimension follow and their general properties are deduced. Many examples are analysed to show some of the more surprising or pathological aspects of dimension theory. Wherever it is useful to do so, proofs are given in detail.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 444

Добавлена в каталог: 28.10.2010

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Предметный указатель

$C^{n}(X)$       92
$F_{\sigma}$ -set      19
$G_{\delta}$ -set      19
$J(\tau)$ , the metrizable hedgehog      86
$T_{3}$ -space      9
$T_{4}$ -space      17
$\beta$ -closed set      49
$\sigma$ -discrete family      11
$\sigma$ -locally finite family      11
Accumulation point      4
Algebra      69
Algebra, complete normed      371
Algebra, normed      371
Almost-open mapping      207
Analytic base      390
Analytic dimension ad      390
Analytic subalgebra      387
Analytic subalgebra L[H]      388
Baire space $B(\tau)$       84
Baire’s theorem      93
Bank of a family of sets      145
Base for a topology      3
Bicompact space      37
Bicompactification      42
Bicompactification, Stone — Cech      46
Bing’s theorem      80
Boundary      12
Brouwer theorem      10
C(X)      92
Canonical covering      214
Canonical mapping into a nerve      108
Canonical mapping of an inverse system      52
Cantor manifold      362
Cantor set      150
Cantor space, n-dimensional      335
Cauchy sequence      91
Chain      2
Closed covering      4
Closed mapping      6
Closed set      3
Closed subalgebra A[H]      371
Closed unit ball      10
Closure      3
Cofinal subset of a directed set      52
Compact space      35
Complete normed algebra      371
Complete space      91
Completely normal space      27
Completely paracompact space      76
Completely regular space      39
Component      4
Connected space      3
Connecting mapping      52
Constancy set      376
Continuous function      5
Countable sum theorem for covering dimension      125
Countable sum theorem for large inductive dimension      171
Countably paracompact space      66
Covering      4
Covering dimension dim      111
Covering, canonical      214
Covering, closed      4
Covering, numerable      22
Covering, open      4
Covering, shrinkable      20
Cozero-set      18
Cushioned refinement      68
Cut      312
CW-complex      296
Decomposing mapping      398
Dense set      4
Diameter, diam      77
Dimension of a CW-complex      297
Dimension of a distributive lattice      366
Dimension of a mapping      336
Dimension of a simplicial complex      105
Dimension, $\delta$       217
Dimension, $\partial im$       368
Dimension, analytic, ad      390
Dimension, approximation      238
Dimension, at a point      197
Dimension, cofinal approximation      238
Dimension, covering, dim      111
Dimension, large inductive, Ind      155
Dimension, local inductive, locInd      188
Dimension, local, locdim      188
Dimension, small inductive, ind      150
Dimensional rank dr      378
Dimensional weight dw      404
Directed family of coverings      215
Directed set      1
Discrete family      11
Discrete topology      3
Distributive lattice      2
Dominated space, by a covering      14
Embedding      7
Envelopment      391
Equivalent bicompactifications      43
Equivalent pseudo-metrics      77
Euclidean n-space $R^{n}$       10
Examples, $T_{4}$ space M such that dim M = Ind M > 0 and ind M = 0      203
Examples, $T_{4}$ -space for which the subset theorem fails for local dimension      203
Examples, $T_{4}$ -space X such that $ind X \neq ind \beta X$       234
Examples, $T_{4}$ -space Z such that ind Z = 0, dim Z = 1 and Ind Z = 2      208
Examples, bicompact space for which the subset theorem does not hold for dim or Ind      161
Examples, bicompact space S such that dim S = 1 and ind S = Ind S = 2      165
Examples, bicompact space X such that ind X = 2 and Ind X = 3      329
Examples, completely normal $T_{3}$ -space which is not totally normal      33
Examples, dimension of a subspace of R      152
Examples, dimension of the rational points in Hilbert space; a totally disconnected space of positive dimension      153
Examples, dimension of the unit interval      113
Examples, metrizable space P such that ind P = 0 and dim P = 1      288
Examples, metrizable space which is not strongly metrizable      86
Examples, strongly metrizable space which is not strongly paracompact      84
Examples, Tihonov space Y such that $dim Y \neq dim \beta Y$       234
Examples, Tihonov space Y such that $dim Y \neq \partial im Y$       368
Examples, totally normal space which is not perfectly normal      73
Examples, zero-dimensional completely normal space with an open subspace of positive dimension      139
Examples, zero-dimensional normal space which is not weakly paracompact      130
Examples, zero-dimensional open mapping which lowers dimension      348
Examples, zero-dimensional spaces with product of positive dimension      354
Extension      19
F-product      357
Face of a simplex      105
Family of functions, separating points      40
Family of functions, separating points from closed sets      40
Filippov’s example      308ff
Fine family of coverings      216
Finite intersection property      35
First-countable space      82
Generalized $F_{\sigma}$ -set      28
Geometric realization      106
Greatest lower bound      1
Hausdorff space      8
Hedgehog $J(\tau)$       86
Hereditarily paracompact space      73
Hilbert cube      88
Hilbert space      88
Homeomorphism      6
Homeomorphism, local      190
Homomorphism of algebras      370
Homomorphism of normed algebras      371
Homotopic mappings      121
Homotopy      121
I, unit interval      5
Ideal of a distributive lattice      49
Ideal of an algebra      370
Identification mapping      8
Identification topology      7
Image of a homomorphism      370

Ind, large inductive dimension      155
ind, small inductive dimension      150
Independent family of sets      144
Inessential mapping      127
Infimum      1
Interior      3
interval      2
Interval topology      4
Inverse limit      52
Inverse system      52
Irreducible mapping      218
Isometry      371
Kernel of a homomorphism      370
Kuratowski lemma      2
Large inductive dimension Ind      155
Lattice      2
Least upper bound      1
Light mapping      398
Lindeloef space      75
Linear order      2
Linearly ordered set      2
Linearly ordered space      5
Local dimension locdim      188
Local homeomorphism      190
Local inductive dimension locInd      188
Locally finite family      11
Long line      163
Lower bound      1
Mapping      5
Mapping, $\mathscr{U}$ -, where $\mathscr{U}$ is an open covering      90
Mapping, almost-open      207
Mapping, canonical, into a nerve      108
Mapping, canonical, of an inverse system      52
Mapping, closed      6
Mapping, connecting      52
Mapping, continuous      5
Mapping, decomposing      398
Mapping, dimension-lowering      340
Mapping, dimension-raising      344
Mapping, identification      8
Mapping, inessential      127
Mapping, irreducible      218
Mapping, light      398
Mapping, open      6
Mapping, perfect      94
Mapping, special irreducible      311
Mapping, zero-dimensional w.r.t. an open covering      392
Maximal element of a partially ordered set      1
Maximal ideal of a distributive lattice      49
Maximal ideal of an algebra      370
Maximal ideal space      50
Mesh of a covering      253
Metric      9
Metric space      9
Metrizable space      10
Minimal element of a partially ordered set      1
Monotone scale of an N-space      288
Monotonicity of dimension      138ff 193ff
N, set of positive integers      3
n-Space      288
Nagata — Smirnov theorem      78
Neighbourhood      3
Nerve of a covering      108
Normal space      17
Normally situated set      28
Normed algebra      371
Numerable covering      22
Open ball      9
Open covering      4
Open mapping      6
Open refinement      4
Open set      3
Open-and-closed set      3
Order of a family of sets      111
Order-complete linearly ordered set      2
Paracompact M-space      101
Paracompact space      57
Partial order      1
Partially ordered set      1
Perfect mapping      94
Perfectly normal space      33
Perfectly zero-dimensional space      217
Point-finite family      11
Polyhedron      108
Precedence, partial order of bicompactifications      43
Pseudo-metric      9
Pseudo-metric space      9
Pseudo-metric topology      9
Pseudo-metrizable space      9
Quasi-order      1
Quasi-ordered set      1
Quotient space      8
R, set of real numbers      5
Rank rk of a subset of a normed algebra      390
refinement      4
Refinement, closed      4
Refinement, cushioned      68
Refinement, open      4
Refinement, star-      70
Refinement, strong star-      70
Refinement, weak      76
Regular family of coverings      216
Regular space      8
Replica of an N-space      290
retract      7
Retraction      7
Roy’s example      271ff
Separable space      86
Separation axioms      8
Separation of sets      119
Shrinkable covering      20
Similar families      24
simplex      105
Simplicial complex      105
Skeleton of a simplicial complex      106
Small inductive dimension ind      150
Space, $T_{i}$ -space, i = 0,1,2      8
Space, Baire      84
Space, bicompact      37
Space, Cantor      335
Space, compact      35
Space, complete      91
Space, completely normal      27
Space, completely paracompact      76
Space, completely regular      39
Space, countably paracompact      66
Space, dominated by a covering      14
Space, Euclidean      10
Space, first-countable      82
Space, Hausdorff      8
Space, hereditarily paracompact      73
Space, Hilbert      88
Space, Lindeloef      75
Space, linearly ordered      5
Space, metric      9
Space, metrizable      10
Space, normal      17
Space, paracompact      57
Space, perfectly normal      33
Space, perfectly zero-dimensional      217
Space, pseudo-metrizable      9
Space, quotient      8
Space, regular      8
Space, separable      86
Space, strongly paracompact      74
Space, strongly pseudo-metrizable      83
Space, Tihonov      39
Space, topological      3
Space, totally disconnected      112
Space, totally normal      31

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