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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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
G-spectrum      321
Group (topological)      292
Homomorphism, of a $\nu$-algebra      37
Homomorphism, of an algebra      5
Homomorphism, structural      381
Image-range of a mapping      2
Indication      3
Indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \Theta)$-normal      196
Indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \Theta, \Delta)$-normal      196
Indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \vartheta)$-normal      182
Indication, $(\vartheta_{\vee},\vartheta_{\wedge}, \vartheta, \vartheta_{\mathcal{F}}, m)$-normal      225
Indication, natural      467
Indicial mapping, general      347
Indicial mapping, of a co-extension      7
Indicial mapping, of an extension      6
Initial co-mark for $(\nu,\mu)$-saturated classes      85
Initial co-mark for $\omega$-saturated classes      411
Initial co-mark for classes of bases      74
Initial co-mark for classes of diagrams      273
Initial co-mark for classes of mappings      258
Initial co-mark for classes of p-bases      79
Initial co-mark for classes of spaces      51
Initial co-mark for classes of spaces with structure      153
Initial co-mark for classes of subsets      56
Initial D-co-mark (for diagrams)      273
Initial F-co-mark for classes of G-spaces      302
Initial F-co-mark for classes of G-subsets      311
Initial F-co-mark for classes of mappings      245
Initial F-co-mark for classes of Y-mappings      258
Initial family for $(\nu, \mu)$-saturated classes      85
Initial family for $\omega$-saturated classes      411
Initial family for classes of bases      74
Initial family for classes of diagrams      273
Initial family for classes of G-diagrams      327
Initial family for classes of G-spaces      302
Initial family for classes of G-subsets      311
Initial family for classes of mappings      245
Initial family for classes of p-bases      79
Initial family for classes of spaces      51
Initial family for classes of spaces with structure      153
Initial family for classes of subsets      56
Initial family for classes of Y-mappings      258
Initial G-D-co-mark      327
Intersection of classes      2
Intersection of restrictions      30
Intersection, property      x
Inverse, element of a group      292
Inverse, mapping of a group      292
Inverse, of a mapping      2
Isometry      391
Isomorphic sets      68
Isomorphism of $\nu$-algebras      37
Isomorphism of algebras      5
Isomorphism of diagrams      266
Isomorphism of s-algebras      13 39
Isomorphism of s-algebras, natural      13 39
Isomorphism, structural      382
Level of an element      67
Mapping      2
Mapping of      2
Mapping of, a space into a spectrum      338
Mapping of, a space into the limit space      338
Mapping of, a space into the limit space, induced      338
Mapping of, Containing Spaces      351
Mapping of, Containing Spaces, equivariant      321
Mapping of, Containing Spaces, natural      351
Mapping of, limit spaces      339
Mapping of, limit spaces, natural      339
Mapping of, spectrum      275
Mapping of, spectrum, structural      381
Mapping, $\alpha$(add)-Borel      501
Mapping, $\alpha$(mult)-Borel      501
Mapping, $\nu$-directing      66
Mapping, $\Phi$-operational      69
Mapping, base-closed      248
Mapping, Borel      501
Mapping, c-base-closed      248
Mapping, closed      248
Mapping, equivariant      301
Mapping, general indicial      347
Mapping, isometric      391
mapping, one-to-one      2
Mapping, onto      2
Mapping, open      248
Mark of a space      5
Mark of a space, $\kappa$-generalized      435
Mark of a space, generalized      435
Morphism of diagrams      266
Morphism of diagrams, equivariant      321
Morphism of diagrams, structural      382
n-tuple      2
Natural embedding of a space      23 45 400
Natural embedding of a specific subset      27
Net-function      421
Net-function of a space      421
Order      4
Order, of a cover      144
Order, partial      4
Order, well ordering      4
Ordinal      3
Ordinal, $\nu$-accessible      171
Ordinal, countable      4
Ordinal, isolated      3
Ordinal, limit      3
p-base      28
pair      2
Pair, $(\bar{M}^G, \bar{M})$      323
Pair, $(\bar{M}^G, \bar{M})$, product-open      323
Pair, $(\bar{M}^G, \bar{M})$, proper      323
Pair, $B^{\lozenge}$-proper      143
Pair, $B^{\vee}$-proper      133
Pair, $N^{\vee}$-proper      133
Pair, $\lambda$-subset-action      316
Pair, B-proper      143
Pair, ordered      2
Pair, space-action      308 316
Pair, subset-action      308
Pair, subset-space      308
Peak of a set      67
Peaked union of $\nu$-sets      68
pos-base      28
Preorder      4
Primary subspace      19
Product mapping of a group      292
Product of classes      2
Projection of an inverse spectrum      275
Projection, limit      337
Proper extension      496
ps-base      28
range of a mapping      2
Range-class      241
Range-restriction of a mapping      157
Refinement of a cover      144
Restriction of a class on the universe      413
Restriction of an indexed collection      7
Restriction of an indexed collection, (M, R)-complete      30
Restriction of an indexed collection, closed      31
Restriction of an indexed collection, complete      59
Restriction of an indexed collection, open      31
Ring      4
Ring, generated      4—5
Ring, minimal      4
Ring, of (subsets of) a set      4
s-algebra of a space      11
S-indexed set of $\omega$-indexed subsets      393
S-indexed set of $\tau$-indexed families      6
S-indexed set of families      6
Saturated class of bases      74
Saturated class of bases, weakly      74
Saturated class of diagrams      273
Saturated class of G-diagrams      326
Saturated class of G-spaces      302
Saturated class of G-spaces with structure      317
Saturated class of G-subsets      310
Saturated class of mappings      245
Saturated class of p-bases      79
Saturated class of p-bases, weakly      79
Saturated class of spaces      51
Saturated class of spaces with structure      153
Saturated class of subsets      56
Saturated class of Y-mappings      258
Saturated class, first-type      367
Saturated class, minimal      451
Saturated class, partially      439
Saturated class, second-type      366—367
Saturated class, simply      440
Saturated class, zero-type      367
Saturation property      xi
Saturation property for an ordinal      90
Saturation property for an ordinal, weak      90
Screening of a pair      179
SEQUENCE      3
Set      1
Set, $\gamma$-peaked      67
Set, $\mathbb{P}$-universal      489
Set, $\tau$-complete      335
Set, A-indexed      3
Set, Borel      65
Set, defining      475 478
Set, directed      4
Set, indexed      2
Set, indexing      3
Set, peaked      67
Set, S-open      346
Set, strongly $\mathbb{P}$-universal      488
Set, well ordered      4
Similar homeomorphism      466
Space, $(\kappa_0, \kappa_1, \theta)$-quotient      486
Space, $(\kappa_0, \kappa_1, \theta, \vartheta)$-quotient      486
Space, $\mathbb{K}$-connectifiable      481
Space, $\mathbb{M}$-complete      473
Space, (Y, $O^*$, I)-separated      265
Space, (Y, O, I)-separated      262
Space, almost regular      480
Space, base $\nu$-dividing      454
Space, completely bounded metric      417
Space, connectifiable      480
Space, containing      vii
Space, countable-dimensional      170
Space, isometrically containing      391
Space, k-weakly n-dimensional      464
Space, locally finite-dimensional      171
Space, marked      5
Space, marked, (S, M)-complete      469
Space, marked, M-complete      469
Space, marked, similar      466
Space, marked, similarly homeomorphic      466
Space, of an inverse spectrum      275
Space, strongly rigid      480
Space, totally disconnected      444
Space, universal      vii 391
Space, Urysohn      480
Space, weakly n-dimensional      459
Space, with structure      152 380
Space-component of a class of $\nu$-sequences      170
Space-component of a class of bases      76
Space-component of a class of G-spaces      301
Space-component of a class of G-spaces with structure      316
Space-component of a class of G-subsets      308
Space-component of a class of p-bases      79
Space-component of a class of spaces with structure      154
Space-component of a class of subsets      61
Space-coordinate of an element of a class of $\nu$-sequences      170
Space-coordinate of an element of a class of bases      76
Space-coordinate of an element of a class of G-spaces      293
Space-coordinate of an element of a class of G-spaces with structure      316
Space-coordinate of an element of a class of G-subsets      308
Space-coordinate of an element of a class of p-bases      79
Space-coordinate of an element of a class of spaces with structure      154
Space-coordinate of an element of a class of subsets      61
Space-singleton      487
Spectrum, $\mathbb{P}$-factorizing      340
Spectrum, $\mathbb{P}$-factorizing, structurally      384
Spectrum, $\mathbb{P}$-factorizing, with respect to a subset      340
Spectrum, $\tau$-continuous      340
Spectrum, $\tau$-continuous, structurally      384
Spectrum, inverse      275
Spectrum, structural      381
strongly      170
Structure on a space      152
Structure-space pair      316
Subset, $\tau$-closed      335
Subset, cofinal      335
Subset, first-type      361
Subset, G-invariant      308
Subset, majorating      335
Subset, second-type      361
Subset, specific      27
Subset, structural      381
Subset, surjective      340
Subset, surjective, structurally      382—383
Subset, zero-type      361
Subset-adjacent class      308
Subset-component of a class of G-subsets      308
Subset-component of a class of p-bases      79
Subset-component of a class of subsets      61
Subset-coordinate of an element of a class of G-subsets      308
Subspectrum      339
Subspectrum, $\tau$-closed      339
Subspectrum, cofinal      339
Supplement      380
Supplement, containing      385—386
Supplement, limit      382—383
Tetrad      2
Topological class of bases      74
Topological class of diagrams      266
Topological class of G-diagrams      322
Topological class of G-spaces      301
Topological class of G-spaces with structure      316
Topological class of G-subsets      308
Topological class of mappings      241
Topological class of p-bases      78
Topological class of spaces      51
Topological class of spaces with structure      152
Topological class of subsets      56
Topological class of Y-mappings      256
Trace on a restriction of a co-mark      7
Trace on a restriction of a family of equivalence relations      8
Trace on a restriction of an equivalence class      8
Trace on a restriction of an equivalence relation      8
Trace on a subset of a base      5
Trace on a subset of an indexed set      5
Triad      2
Uniform class of metric spaces      417
Union of $\nu$-sets      68
Union of $\nu$-sets, peaked      68
Union of classes      2
Union of restrictions      30
Union, structural free      386
Unit of a group      292
Universal element in a class of $\nu$-sequences      168
Universal element in a class of $\nu$-sequences, properly      168
Universal element in a class of bases      75
Universal element in a class of diagrams      266
Universal element in a class of G-diagrams      327
Universal element in a class of G-spaces      301
Universal element in a class of G-spaces with structure      318
Universal element in a class of G-spaces with structure, properly      318
Universal element in a class of G-subsets      312
Universal element in a class of G-subsets, properly      312
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