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Iliadis S.D. — Universal Spaces and Mappings
Iliadis S.D. — Universal Spaces and Mappings



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Название: Universal Spaces and Mappings

Автор: Iliadis S.D.

Аннотация:

The book is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on. Universal spaces Universal mappings Dimension theory Actions of groups Isometric Universal Spaces

Preface.
Introductory remarks.
Chapter 1. The construction of Containing Spaces.
Chapter 2. Saturated classes.
Chapter 3. Dimension-like functions.
Chapter 4. Saturated classes of spaces with structure.
Chapter 5. Completely regular and compact spaces.
Chapter 6. Saturated classes of mappings.
Chapter 7. Actions of groups.
Chapter 8. Containing Spaces and factorizing T-spectra.
Chapter 9. Isometries and universality.
Chapter 10. Concluding remarks and open problems.brBibliography. Index of symbols. Subject index. AudienceDescription: Researchers in Topology, postgraduate students.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 560

Добавлена в каталог: 22.01.2007

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Предметный указатель
$(s-b^n-Ind < \alpha)$-uniform class      210
$(\beta+n)$-representation      162
$(\Lambda, \prec, p)$-structure      152
$(\lambda_0, \lambda_1)$-component of a diagram      266
$(\nu, \mu)$-saturated class of spaces      85
$(\Phi, \Lambda, \prec, p)$-structure      152
$(\Phi,\Lambda, \prec, p)$-co-structure      153
$2^{\tau}$-saturated class      442
$2^{\tau}$-universality property      442
$F_{\sigma}$-set      65
$G_{\delta}$-set      65
$P_{\sigma}$-space      85
$T_3$-p-base      82
$T_3^c$-p-base      82
$T_3^s$-D-base      82
$\alpha$(add)-BG-space      503
$\alpha$(mult)-BG-space      503
$\alpha$-expansion      194
$\infty$-saturated class      441
$\lambda$-adjacent class of G spaces      316
$\lambda$-component of a diagram      266
$\mathbb{M}$-completion      468
$\mathbb{M}(rs)$-completion      473
$\mathbb{P}$-base      74
$\mathbb{P}$-co-base      74
$\mathbb{P}$-co-p-base      78
$\mathbb{P}$-co-structure      153
$\mathbb{P}$-p-base      78
$\mathbb{P}$-restriction      56
$\mathbb{P}$-spectrum      331
$\mathbb{P}$-spectrum, structural      381
$\mathbb{P}$-structure      152
$\mathbb{P}$-subset      370 385—386
$\mathbb{P}-\tau$-spectrum      341
$\nu$-algebra of a set      37
$\nu$-algebra of a set, minimal      37
$\nu$-sequence      167
$\nu$-set      67
$\nu$-set, free      68
$\omega$-saturated class      410
$\omega$-saturated class, isometric ally      410—411
$\sim$-equivalence class      4
$\sim^R_M$-equivalence relation      15 42
$\sim^s_M$-equivalence relation      14
$\sim^s_m$-equivalence relation, s- standard      13
$\sim^s_m$-equivalence relation, standard      13
$\tau$-formulation      xii
$\tau$-property      xii
$\tau$-spectrum      341
$\tau$-spectrum, structural      384
$\theta$-extension of an indexed set      6
$\varepsilon$-component of a co-mark      346
$\varepsilon$-net      417
(S, M)-completion      468
Action of a group      293
Action of a group, $\alpha$(add)-Borel      502
Action of a group, $\alpha$(mult)-Borel      502
Action of a group, Borel      502
Action of a group, effective      306
Action of a group, free      306
Action of a group, limit      329
Action of a group, on a G-diagram      321
Action-component of a class of G-spaces      301
Action-component of a class of G-spaces with structure      316
Action-component of a class of G-subsets      308
Action-coordinate of a G-space      293
Action-coordinate of a G-space with structure      316
Action-coordinate of an element of a class of G-subsets      308
Adjacent class of G-spaces      308 316
Adjacent class of spaces with structure      316
Adjacent class of subsets      79 308
Admissible, branching triad      195
Admissible, tetrad      225
Admissible, triad      181
Algebra      4
Algebra, generated      4—5
Algebra, minimal      4
Algebra, of a set      4
Base for a space      5
Base for the closed subsets      5
Base for the closed subsets, normal      179
Base for the open subsets      5
Base for the open subsets, normal      180
Base, $(\kappa, \lozenge)$-standard      186
Base, $(\lozenge, \kappa)$-standard      22
Base, $\kappa$-standard      22
Base, $\lozenge$-standard      22
Base, $\nu$-dividing      454
Base, $\tau$-indexed      5
Base, ($b^n-dim < m$)-dimensional      225
Base, ($b^n-Ind < \alpha$)-dimensional      193
Base, base-normal      180
Base, disjunctive      180
Base, positional      28
Base, standard      22
BG-space      503
Branching family of mappings      194
Cardinal      3
Chain      335
CHARACTER      458
class      1
Class in the universe of metric spaces      409
Class in the universe of metric spaces generated      413
Class in the universe of metric spaces, complete      412
Class in the universe of metrizable spaces      409
Class of all bases      74
Class of all p-bases      78
Class of all pos-bases      78
Class of all ps-bases      78
Class of bases      74
Class of G-diagrams generated      328
Class of G-spaces generated      304
Class of G-spaces with structure      315
Class of G-spaces with structure, complete      318
Class of G-spaces with structure, generated      318
Class of G-subsets      308
Class of G-subsets generated      313
Class of G-subsets subset-generated      313
Class of G-subsets, complete      312
Class of p-bases      78
Class of p-bases, closed      79
Class of p-bases, complete      79
Class of p-bases, open      79
Class of spaces with structure      152
Class of spaces with structure, complete      154
Class of subsets      56
Class of subsets, closed      59
Class of subsets, complete      59
Class of subsets, open      59
Class of the limit spaces      277
Class, $\mathbb{B}$-rim-hereditary      92
Class, $\mathbb{B}$-str-rim-hereditary      157
Class, $\mathbb{B}-b^0$-rim- hereditary      113
Class, $\mathbb{B}-b^0-p_0$-rim-hereditary      128
Class, $\mathbb{B}-b^0-p_1$-rim-hereditaiy      128
Class, $\mathbb{B}-b^1$-rim-hereditary      114
Class, $\mathbb{B}-b^1-p_0$-rim-hereditary      129
Class, $\mathbb{B}-b_0$-rim-hereditary      106
Class, $\mathbb{B}-b_0-p_0$-rim-hereditary      125
Class, $\mathbb{B}-b_0-p_1$-rim-hereditary      125
Class, $\mathbb{B}-b_1$-rim-hereditary      112
Class, $\mathbb{B}-b_1-p_1$-rim-hereditary      126
Class, $\mathbb{B}-p_1$-rim-hereditary      104
Class, $\mathbb{D}$-b(l)-rim-hereditary      117
Class, $\mathbb{D}-p_0$-rim-hereditary      97
Class, $\mathbb{D}-p_1$-rim-hereditary      97
Class, $\mathbb{F}$-hereditary      143
Class, $\mathbb{F}-\lozenge$-hereditary      143
Class, $\mathbb{F}-\vee$-hereditary      133
Class, additive      66
Class, b(0)-rim-hereditary      117
Class, corresponding      412
Class, multiplicative      66
Class, structural      380
Class,$\mathbb{B}-b^1-p_1$-rim-hereditary      129
Class,$\mathbb{B}-b_1-p_0$-rim-hereditary      126
Class,$\mathbb{B}-p_0$-rim-hereditary      104
Class,$\mathbb{D}-b^p$-rim-hereditary      115
Co-base, ($b^n-dim < m$)-dimensional      229
Co-base, ($b^n-Ind < \alpha$)-dimensional      203
Co-base, for an indexed collection      6
Co-base, for an indexed collection, closed      6
Co-base, for an indexed collection, open      6
Co-base, normal      185
Co-extension of a D-co-mark      267
Co-extension of a pair ($\bar{M}_0^G$, $\bar{M}_0$)      323
Co-extension of an P-co-mark      242
Co-extension of an S-indexed set      7
Co-extension, general      347
Co-indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \Theta, \Delta)$-normal      204
Co-indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \vartheta)$-normal      182
Co-indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \vartheta, \vartheta_{\mathcal{F}}, m)$-normal      229
Co-indication, of an S-indexed set      6
Co-mark      6
Co-mark, $\kappa$-generalized      435
Co-mark, generalized      435
Co-mark, O-commutative      63
Co-mark, Q-proper      475
Co-mark, Q-regular      478
Co-mark, semi-straight      487
Co-mark, straight      487
Co-operator on a class of spaces      62
Co-operator on a class of spaces, commutative      62 63
Co-operator on a class of spaces, topological      62
Co-p-base      78
Co-pos-base      78
Co-ps-base      78
Co-singleton      474
Co-singleton, closed      474
Co-structure      153
Collection      1
Collection, full indexed      467
Collection, S-indexed      393
Compact resolution      495
Compact resolution, universal      495
Complementary to a base      179
Complementary to a co-base      185
Complementary to a co-indication      185
Complementary to a family      179
Complementary to an indication      179
Completion of an element      67
Component of a co-mark      346
composition      451
Containing Space      19 44
Containing Space, Q-quotient      476
Containing Space, quotient      476
Containing, action-mapping      301
Containing, diagram      271 272
Containing, G-diagram      326
Containing, mapping      244—245
Containing, space      vii
Containing, structure      153
Containing, triad      310 317
Cover of a space      144
D-co-mark (for diagrams)      267
D-co-mark (for diagrams), proper      267
D-mark (for diagrams)      266
defining classes      89
Diagram (commutative)      266
Diagram (commutative), open      289
DIMENSION      89
Dimension, at a point      459
Dimension, dim      144
Dimension, large inductive      132
Dimension, metric      423
Dimension, new      452
Dimension, order      453
Dimension, small inductive      91
Dimension-like function      89
Dimension-like function, base      89
Dimension-like function, base positional      89
Dimension-like function, new      452
Dimension-like function, positional      89
Dimension-like function, space      89
Dimensional kernel      459
Dispersion point      480
Domain of a mapping      2
Domain-class      241
Element, free (of a $\nu$-set)      67
Element, isometrically universal      410
Element, isometrically universal, properly      410
Element, majorating      335
Element, minimal (of an order)      4
Embedding (for classes $\mathbb{P}$($(\beta+n)$-rep.))      164
Embedding (for mappings)      241
Empty Subset Condition      145
Equivalence class      4
Equivalence class, induced      242
Equivalence relation      4
Equivalence relation, s-standard      13
Equivalence relation, standard      13
Expansion of a branching family      194
Extension of an indexed set      6
F-co-mark      242
F-co-mark, product-open      294
F-co-mark, proper      242
F-domain      241
F-image      242
f-image of an (indexed) set      3
F-preimage of a co-mark      241
f-preimage of an (indexed) set      3
F-preimage of an indexed family      256
F-range      241
Family      1
Family of equivalence relations, $(M, \nu)$-standard      41
Family of equivalence relations, $(M, \nu, \mu)$-admissible      41
Family of equivalence relations, $(M, \Psi)$-admissible      153
Family of equivalence relations, $(M^d, M^r)$-admissible      242
Family of equivalence relations, $(\bar{M}^G, \bar{M})$-admissible      324
Family of equivalence relations, $(\kappa, \lozenge)$-standard      186
Family of equivalence relations, $\bar{M}$-admissible      268
Family of equivalence relations, $\mu$-admissible      41
Family of equivalence relations, (M, P)-admissible      394
Family of equivalence relations, (M, Q)-admissible      24
Family of equivalence relations, admissible      8
Family of equivalence relations, compact      495
Family of equivalence relations, generalized      437
Family of equivalence relations, induced      242
Family of equivalence relations, M-admissible      15
Family of equivalence relations, M-standard      15
Family of equivalence relations, O-commutative      63
Family, $(\lozenge, \kappa)$-standard      22
Family, $\kappa$-standard      22
Family, $\lozenge$-standard      22
Family, $\mathbb{F}$-(Y, $O^*$, I)-separating      265
Family, $\mathbb{F}$-(Y, O, I)-separating      265
Family, (Y, $O^*$, I)-separating      265
Family, (Y, O, I)-separating      262
Family, standard      22
Filter      212
Filter, maximal      212
Final refinement      8 41
Finite Free Union Condition      134
Finite Union Condition      145
Function      2
Function, cardinal-algebra      433
G-space, Borel      503
G-space, limit      329
G-space, with $(\Phi, \Lambda, \prec, p)$-structure      315
G-space, with structure      315
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