International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 367-375
-point finite refinable spaces
229 Vincent Science Hall, Slippery Rock, PA 16057-1326, USA
Received 4 October 1996; Revised 28 October 1996
Copyright © 1999 Sheldon W. Davis et al. 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.
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.