On the product of twob f-spaces

“…It is easy to see that B is a proper subclass of the class of all pseudocompact spaces. The spaces X ∈ B admit the following nice characterization [13,5,42]: for every sequence {U n : n ∈ ω} of disjoint non-empty open subsets of X, there is an infinite subset J ⊆ ω such that for any filter ξ on J, the set F ∈ξ n∈F U n is not empty. By [38, Corollary 2.14], every pseudocompact topological group is in B.…”

Section: Corollary 16 a Countably Compact Tikhonov Space With A Conmentioning

confidence: 99%

Selections and suborderability

et al. 2002

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Abstract. We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set. Extending Fujii-Nogura results, we show that an almost compact space with a continuous zero-selection is homeomorphic to some ordinal space, and a (locally compact) pseudocompact space with a continuous zero-selection is an (open) subspace of some space of ordinals. Under the Diamond Principle, we construct several counterexamples, e.g. a locally compact locally countable monotonically normal space with a continuous zero-selection which is not suborderable.

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“…Define now a function g μ B from G × cl μX B into μX as g μ B (g, x) = g A,B (g, x) whenever g ∈ A with A a bounded subset of G. It is straightforward that g μ B is well-defined and b f -continuous. Since cl μX B is compact, G × cl μX B is a b f -space[7, Theorem 9], so that g μ B is continuous. Next define a function h on G × μX as h(g, x) = g μ B (g, x) whenever x ∈ cl μX B for some bounded subset B of X.…”

mentioning

confidence: 99%

Dieudonné completion and bf-group actions

González

Sanchis

2006

Topology and its Applications

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If G(X) denotes either the free topological group or the free Abelian topological group over a topological space X, we prove that n i=1 G(X i ) is a hemibounded b f -group whenever each X i is a pseudocompact space (which provides a new way to generate this kind of topological groups), and we show that the equality μ(holds whenever X is a hemibounded b f -space (where μY stands for the Dieudonné completion of Y ). By means of the Dieudonné completion we prove that every pseudocompact space X is G-Tychonoff whenever G is a b f -group and that the maximal G-compactification of X coincides with βX. We apply this result to obtain a partial version for G-spaces of Glicksberg's theorem on pseudocompactness and we analyze when the maximal G-compactification of a G-space X coincides with the Stone-Čech compactification of X in the case when G is a metrizable group.

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On the product of twob f-spaces

Cited by 12 publications

References 11 publications

Completeness, metrizability and compactness in spaces of fuzzy-number-valued functions

Completeness, metrizability and compactness in spaces of fuzzy-number-valued functions

Selections and suborderability

Dieudonné completion and bf-group actions

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