Bulletin of the Belgian Mathematical Society - Simon Stevin, ISSN 1370-1444, 07/2007, Volume 14, Issue 3, pp. 555 - 564

.... We obtain a Banach-Stone type theorem between Baire functions defined on completely regular spaces...

Banach-Stone theorem | Baire functions | Banach algebras | Borel functions | Completely regular spaces | MATHEMATICS | completely regular spaces | 46E15 | 46J10 | 46B04 | 54C35

Banach-Stone theorem | Baire functions | Banach algebras | Borel functions | Completely regular spaces | MATHEMATICS | completely regular spaces | 46E15 | 46J10 | 46B04 | 54C35

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2008, Volume 136, Issue 8, pp. 2985 - 2995

Given a Lie group G we study the class \mathcal {M}_G of proper metrizable G-spaces with metrizable orbit spaces, and show that any G-space X \in \mathcal {M...

Isotropy | Embeddings | Mathematical theorems | Topological theorems | Completely regular spaces | Homeomorphism | Lie groups | Topology | Proper actions | Equivariant embedding | Tubular covering | MATHEMATICS | MATHEMATICS, APPLIED | PROPER G-SPACES | proper actions | equivariant embedding | tubular covering

Isotropy | Embeddings | Mathematical theorems | Topological theorems | Completely regular spaces | Homeomorphism | Lie groups | Topology | Proper actions | Equivariant embedding | Tubular covering | MATHEMATICS | MATHEMATICS, APPLIED | PROPER G-SPACES | proper actions | equivariant embedding | tubular covering

Journal Article

Filomat, ISSN 0354-5180, 1/2014, Volume 28, Issue 6, pp. 1237 - 1246

The existence of fixed points for continuous mappings on general topological spaces via compact subsets is proved...

Topological theorems | Real numbers | Coincidence | Completely regular spaces | General topology | Topological spaces | Continuous functions | Lower semi continuous function from above | Coincidence point | Compact topological space | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | THEOREMS | lower semi continuous function from above | compact topological space

Topological theorems | Real numbers | Coincidence | Completely regular spaces | General topology | Topological spaces | Continuous functions | Lower semi continuous function from above | Coincidence point | Compact topological space | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | THEOREMS | lower semi continuous function from above | compact topological space

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2016, Volume 207, Issue 11, pp. 1562 - 1581

.... For a finite-dimensional orbit space a reduction of the Hilbert-Smith conjecture to certain other problems in geometric topology is presented...

Free action of a group | K-theory | Lens spaces | Completely regular maps | completely regular maps | EQUIVARIANT MAPS | SPACES | SPHERES | REGULAR MAPPINGS | lens spaces | TRANSFORMATION GROUPS | MATHEMATICS | HOMEOMORPHISMS | DIMENSION | CATEGORY | ANR FIBERS | free action of a group | Reduction | Topology | Mathematical analysis | Manifolds (mathematics) | Lie groups | Lenses | Mathematics - Algebraic Topology

Free action of a group | K-theory | Lens spaces | Completely regular maps | completely regular maps | EQUIVARIANT MAPS | SPACES | SPHERES | REGULAR MAPPINGS | lens spaces | TRANSFORMATION GROUPS | MATHEMATICS | HOMEOMORPHISMS | DIMENSION | CATEGORY | ANR FIBERS | free action of a group | Reduction | Topology | Mathematical analysis | Manifolds (mathematics) | Lie groups | Lenses | Mathematics - Algebraic Topology

Journal Article

5.
Full Text
Completely regularly ordered spaces versus T2-ordered spaces which are completely regular

Topology and its Applications, ISSN 0166-8641, 2004, Volume 135, Issue 1, pp. 185 - 196

...) is completely regular need not be a completely regularly ordered space (that is, T 3.5+ T 2-ordered ⇏T 3.5 -ordered). We show that a completely regular T 2-ordered space...

Order-convex | Increasing continuous real-valued function | Completely regularly ordered | Topological ordered space | Completely regular

Order-convex | Increasing continuous real-valued function | Completely regularly ordered | Topological ordered space | Completely regular

Journal Article

Topology and its Applications, ISSN 0166-8641, 08/2012, Volume 159, Issue 12, pp. 2888 - 2898

We establish that every second countable completely regularly preordered space (E,T,⩽) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p...

Quasi-uniformities | Quasi-pseudo-metrics | Completely regularly ordered spaces | MATHEMATICS | MATHEMATICS, APPLIED | ORDERED SPACES | BITOPOLOGICAL SPACES | Mathematics - General Topology

Quasi-uniformities | Quasi-pseudo-metrics | Completely regularly ordered spaces | MATHEMATICS | MATHEMATICS, APPLIED | ORDERED SPACES | BITOPOLOGICAL SPACES | Mathematics - General Topology

Journal Article

Topology and its Applications, ISSN 0166-8641, 2004, Volume 143, Issue 1, pp. 27 - 48

... of all completely regular spaces is discussed.

Space | Function | Dimension | Completely regular | MATHEMATICS | completely regular | MATHEMATICS, APPLIED | dimension | space | function

Space | Function | Dimension | Completely regular | MATHEMATICS | completely regular | MATHEMATICS, APPLIED | dimension | space | function

Journal Article

Topology and its Applications, ISSN 0166-8641, 05/2013, Volume 160, Issue 8, pp. 965 - 978

In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions...

Quasi-uniformities | Quasi-pseudo-metrics | Completely regularly ordered spaces | SPACETIMES | MATHEMATICS | TOPOLOGICAL-SPACES | ORDER | MATHEMATICS, APPLIED | TIME | BITOPOLOGICAL SPACES | METRIZATION

Quasi-uniformities | Quasi-pseudo-metrics | Completely regularly ordered spaces | SPACETIMES | MATHEMATICS | TOPOLOGICAL-SPACES | ORDER | MATHEMATICS, APPLIED | TIME | BITOPOLOGICAL SPACES | METRIZATION

Journal Article

Economic Theory, ISSN 0938-2259, 7/2005, Volume 26, Issue 1, pp. 129 - 139

.... For the problem of incomplete information, Harsányi suggested the concept of the type space. Later Mertens and Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space...

Topological regularity | Topological theorems | Completely regular spaces | Homeomorphism | Coordinate systems | Mathematical functions | Topology | Topological spaces | Borel sets | Cylinders | Economics general | Coherent beliefs | Analysis | Economic Theory | Incomplete information | Type space | Economics / Management Science | BELIEFS | ECONOMICS | incomplete information | type space | coherent beliefs | Studies | Economic theory | Game theory

Topological regularity | Topological theorems | Completely regular spaces | Homeomorphism | Coordinate systems | Mathematical functions | Topology | Topological spaces | Borel sets | Cylinders | Economics general | Coherent beliefs | Analysis | Economic Theory | Incomplete information | Type space | Economics / Management Science | BELIEFS | ECONOMICS | incomplete information | type space | coherent beliefs | Studies | Economic theory | Game theory

Journal Article

B-순수 및 응용수학, ISSN 1226-0657, 2003, Volume 10, Issue 1, pp. 25 - 35

We study equivalent definitions and some categorical properties of completely regular quasi-ordered spaces and zero-dimensional quasi-ordered spaces...

o-completely regular filters | compact zero-dim | reflection | an universal initial completion | zero-dimensional quasi-ordered spaces | o-zero-dimensional filters | MacNeille completion | compact partially ordered spaces | completely regular quasi-ordered spaces

o-completely regular filters | compact zero-dim | reflection | an universal initial completion | zero-dimensional quasi-ordered spaces | o-zero-dimensional filters | MacNeille completion | compact partially ordered spaces | completely regular quasi-ordered spaces

Journal Article

The Journal of Symbolic Logic, ISSN 0022-4812, 12/2010, Volume 75, Issue 4, pp. 1137 - 1146

Introduction. In 1937 E. Čech and M.H. Stone, independently, introduced the maximal compactification of a completely regular topological space, thereafter called Stone...

Mathematical set theory | Impredicativity | Mathematical sets | Compactification | Completely regular spaces | Boolean data | Mathematical logic | General topology | Uniformity | Topological spaces | MATHEMATICS | GENERAL TOPOLOGY | LOCALES | Uniformity of nature | Fuzzy sets | Usage | Analysis | Set theory | Algebra, Boolean

Mathematical set theory | Impredicativity | Mathematical sets | Compactification | Completely regular spaces | Boolean data | Mathematical logic | General topology | Uniformity | Topological spaces | MATHEMATICS | GENERAL TOPOLOGY | LOCALES | Uniformity of nature | Fuzzy sets | Usage | Analysis | Set theory | Algebra, Boolean

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2005, Volume 133, Issue 11, pp. 3421 - 3427

In this paper, we obtain several new continuous selection theorems for multi-valued mappings on completely regular spaces and fixed point theorems for multi-valued maps on nonmetrizable spaces...

Mathematical theorems | Topological theorems | Economic theory | Completely regular spaces | Diagonal lemma | Topological vector spaces | Index sets | Continuous functions | Topological spaces | Fixed points | Multi-valued mappings | Continuous selections | MATHEMATICS | MATHEMATICS, APPLIED | continuous selections | fixed points | MULTIFUNCTIONS | EQUILIBRIA | THEOREMS | multi-valued mappings | APPROXIMATE SELECTION | VALUED MAPPINGS

Mathematical theorems | Topological theorems | Economic theory | Completely regular spaces | Diagonal lemma | Topological vector spaces | Index sets | Continuous functions | Topological spaces | Fixed points | Multi-valued mappings | Continuous selections | MATHEMATICS | MATHEMATICS, APPLIED | continuous selections | fixed points | MULTIFUNCTIONS | EQUILIBRIA | THEOREMS | multi-valued mappings | APPROXIMATE SELECTION | VALUED MAPPINGS

Journal Article

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 06/2019, Volume 26, Issue 2, pp. 255 - 273

In this paper, we introduce two new concepts, namely, a subset being d(delta)-connected relative to a topological space, and a subset being D-delta-closed relative to the space...

MATHEMATICS | D-delta-closed relative to a space | D-delta-completely regular space | d(delta)-connected relative to a space | d(delta)-separation relative to a space | d(delta)-quasicomponent of a subset relative to a space

MATHEMATICS | D-delta-closed relative to a space | D-delta-completely regular space | d(delta)-connected relative to a space | d(delta)-separation relative to a space | d(delta)-quasicomponent of a subset relative to a space

Journal Article

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, 9/2017, Volume 72, Issue 5, pp. 267 - 275

The present paper is a continuation of the author’s paper [1], where by means of a special integral representation of functions we prove embedding theorems for multianisotropic functional spaces. In contrast to [1...

multianisotropic space | 32Q40 | completely regular polyhedron | Mathematics, general | Mathematics | Embedding theorem | integral representation

multianisotropic space | 32Q40 | completely regular polyhedron | Mathematics, general | Mathematics | Embedding theorem | integral representation

Journal Article

Glasnik Matematicki, ISSN 0017-095X, 05/2010, Volume 45, Issue 1, pp. 173 - 217

If (C, D) is a category pair such that D subset of C is a pror eflective subcategory, then so is D subset of pro-C and, inductively, D subset of pro(n)C as...

Polyhedron | Pro-pro-category | Completely regular space | Pro-category | Shape | Compact hausdorff space | Pro-reflective subcategory | Stone- Čech compactification | Expansion | Hewitt realcompactification | MATHEMATICS | MATHEMATICS, APPLIED | polyhedron | shape | completely regular space | pro-pro-category | compact Hausdorff space | Stone-Cech compactification | pro-reflective subcategory | expansion | Stone-Čech compactification

Polyhedron | Pro-pro-category | Completely regular space | Pro-category | Shape | Compact hausdorff space | Pro-reflective subcategory | Stone- Čech compactification | Expansion | Hewitt realcompactification | MATHEMATICS | MATHEMATICS, APPLIED | polyhedron | shape | completely regular space | pro-pro-category | compact Hausdorff space | Stone-Cech compactification | pro-reflective subcategory | expansion | Stone-Čech compactification

Journal Article

16.
Full Text
Proving the Banach–Alaoglu Theorem via the Existence of the Stone–Čech Compactification

The American Mathematical Monthly, ISSN 0002-9890, 2/2014, Volume 121, Issue 2, pp. 167 - 169

.... In this note, the theorem is proved by assuming the existence of the Stone–Čech compactification for completely regular topological spaces.

NOTES | Mathematical theorems | Topological theorems | Logical theorems | Compactification | Existence theorems | Completely regular spaces | Functional analysis | General topology | Topological spaces | MATHEMATICS | SPACES | Theorems (Mathematics) | Usage | Banach spaces | Proof theory | Analysis

NOTES | Mathematical theorems | Topological theorems | Logical theorems | Compactification | Existence theorems | Completely regular spaces | Functional analysis | General topology | Topological spaces | MATHEMATICS | SPACES | Theorems (Mathematics) | Usage | Banach spaces | Proof theory | Analysis

Journal Article

Order, ISSN 0167-8094, 09/1990, Volume 7, Issue 3, pp. 283 - 293

We present an example of a completely regular ordered space that is not strictly completely regular ordered...

AMS subject classifications : 6F30, 54F05, 54E15 | I-space | pairwise completely regular | Completely regular ordered space | MATHEMATICS | PAIRWISE COMPLETELY REGULAR | I-SPACE | COMPLETELY REGULAR ORDERED SPACE

AMS subject classifications : 6F30, 54F05, 54E15 | I-space | pairwise completely regular | Completely regular ordered space | MATHEMATICS | PAIRWISE COMPLETELY REGULAR | I-SPACE | COMPLETELY REGULAR ORDERED SPACE

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2003, Volume 62, Issue 1-2, pp. 1 - 6

... when restricted to strictly completely regular bitopological spaces.

Strictly completely regular bitopological spaces | Nachbin ordered compactification | Strictly completely regular ordered space | Universal bicompactification | MATHEMATICS | strictly completely regular ordered space | strictly completely regular bitopological spaces | universal bicompactification

Strictly completely regular bitopological spaces | Nachbin ordered compactification | Strictly completely regular ordered space | Universal bicompactification | MATHEMATICS | strictly completely regular ordered space | strictly completely regular bitopological spaces | universal bicompactification

Journal Article

19.
Strict complete regularity in the categories of bitopological spaces and ordered topological spaces

Publicationes Mathematicae, ISSN 0033-3883, 2001, Volume 58, Issue 4, pp. 693 - 705

We introduce the notion of a strictly completely regular bitopological space and show that the category of strictly completely regular bitopological spaces is isomorphic to the category of strictly...

Quasi-uniform space | Completely regular bitopological space | Completely regular topological ordered space | Strictly completely regular bitopological space | Strictly completely regular ordered space | MATHEMATICS | strictly completely regular ordered space | strictly completely regular bitopological space | completely regular bitopological space | quasi-uniform space | completely regular topological ordered space

Quasi-uniform space | Completely regular bitopological space | Completely regular topological ordered space | Strictly completely regular bitopological space | Strictly completely regular ordered space | MATHEMATICS | strictly completely regular ordered space | strictly completely regular bitopological space | completely regular bitopological space | quasi-uniform space | completely regular topological ordered space

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/1980, Volume 262, Issue 2, pp. 437 - 446

.... It is shown here that these spaces, called D-completely regular, can be generated from a single second countable developable space D which has the same cardinality as the reals...

Topological regularity | Mathematical theorems | Second countable spaces | Completely regular spaces | Regular spaces | Respect | General topology | Topological spaces | Continuous functions | Perfect spaces | Epireflective hull | Developable spaces | ö-completely regular spaces | 7?-normal spaces | Simple category

Topological regularity | Mathematical theorems | Second countable spaces | Completely regular spaces | Regular spaces | Respect | General topology | Topological spaces | Continuous functions | Perfect spaces | Epireflective hull | Developable spaces | ö-completely regular spaces | 7?-normal spaces | Simple category

Journal Article

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