International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1999 / Article

Open Access

Volume 22 |Article ID 426935 | https://doi.org/10.1155/S0161171299223678

Sheldon W. Davis, Elise M. Grabner, Gray C. Grabner, "s-point finite refinable spaces", International Journal of Mathematics and Mathematical Sciences, vol. 22, Article ID 426935, 9 pages, 1999. https://doi.org/10.1155/S0161171299223678

s-point finite refinable spaces

Received04 Oct 1996
Revised28 Oct 1996

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) CX,(i) for all nonempty V𝒱,VC and(ii) for all aC the set (𝒱)a={V𝒱:aV} is finite.In this paper we distinguish these spaces, study their basic properties and raise several interesting questions. If λ is an ordinal with cf(λ)=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.

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.


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