Displaying similar documents to “Mesocompactness and selection theory”

Compact images of spaces with a weaker metric topology

Peng-fei Yan, Cheng Lü (2008)

Czechoslovak Mathematical Journal

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If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology. In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that (1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence { ℱ i } i ∈ ℕ of point-finite c s -covers such that ⋂ i ∈ ℕ st ( y , ℱ i ) = { y } for each y ∈ Y . (2) Y is...

Weak-bases and D -spaces

Dennis K. Burke (2007)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that certain weak-base structures on a topological space give a D -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Hence, quotient mappings, with compact fibers, from metric spaces have a D -space image. What about quotient s -mappings? Arhangel’skii and Buzyakova have shown that spaces with a point-countable base...

Sequential completeness of subspaces of products of two cardinals

Roman Frič, Nobuyuki Kemoto (1999)

Czechoslovak Mathematical Journal

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Let κ be a cardinal number with the usual order topology. We prove that all subspaces of κ 2 are weakly sequentially complete and, as a corollary, all subspaces of ω 1 2 are sequentially complete. Moreover we show that a subspace of ( ω 1 + 1 ) 2 need not be sequentially complete, but note that X = A × B is sequentially complete whenever A and B are subspaces of κ .

Generalized tri-quotient maps and Čech-completeness

Themba Dube, Vesko M. Valov (2001)

Commentationes Mathematicae Universitatis Carolinae

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For a topological space X let 𝒦 ( X ) be the set of all compact subsets of X . The purpose of this paper is to characterize Lindelöf Čech-complete spaces X by means of the sets 𝒦 ( X ) . Similar characterizations also hold for Lindelöf locally compact X , as well as for countably K -determined spaces X . Our results extend a classical result of J. Christensen.