Sheldon W. Davis, Elise M. Grabner, Gray C. Grabner, "-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
-point finite refinable spaces
A space is called -point finite refinable (-point finite refinable) provided every open cover of has an open refinement such that, for some (closed discrete) ,(i) for all nonempty and(ii) for all the set is finite.In this paper we distinguish these spaces, study their basic properties and raise several interesting questions. If is an ordinal with and is a stationary subset of then is not -point finite refinable. Countably compact -point finite refinable spaces are compact. A space is irreducible of order if and only if it is -point finite refinable. If is a strongly collectionwise Hausdorff -point finite refinable space without isolated points then is irreducible.
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