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International Journal of Mathematics and Mathematical Sciences - Volume 22 1999, Issue 2, Pages 367-375

229 Vincent Science Hall, Slippery Rock, PA 16057-1326, USA

Received 4 October 1996; Revised 28 October 1996

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A space X is called s-point finite refinable ds-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 𝒱a={V∈𝒱:a∈V} is finite.

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





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

Fuente: https://www.hindawi.com/



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