s -point finite refinable spaces

Sheldon W. Davis, Elise M. Grabner and Gray C. Grabner

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-9

Abstract:

A space X is called s -point finite refinable ( d s -point finite refinable) provided every open cover 𝒰 of X has an open refinement 𝒱 such that, for some (closed discrete) C ⫅ X ,

(i) for all nonempty V ∈ 𝒱 , V ∩ C ≠ ∅ and

(ii) for all a ∈ C the set ( 𝒱 ) a = { V ∈ 𝒱 : a ∈ V } is finite.

In this paper we distinguish these spaces, study their basic properties and raise several interesting questions. If λ is an ordinal with c f ( λ ) = λ > ω and S is a stationary subset of λ then S is not s -point finite refinable. Countably compact d s -point finite refinable spaces are compact. A space X is irreducible of order ω if and only if it is d s -point finite refinable. If X is a strongly collectionwise Hausdorff d s -point finite refinable space without isolated points then X is irreducible.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:426935

DOI: 10.1155/S0161171299223678

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