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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Some Weak Covering Properties Related to Metacompactness
by
Gary and Elise Grabner
Slippery Rock University

A space X is said to be A-refinable (AD-refinable) provided every open cover U of X has an open refinement V such that for some (discrete) set A subset or equal X,

  1. V \cap A =/= \phi for all V in V

  2. {V in V : x in V } is finite for all x in A.

We will discuss basic properties of these spaces and present several open questions.

Theorem. A space is AD-refinable if and only if it is irreducible of order \omega0.

Theroem. If X is the perfect preimage of an A-refinable space then every directed open cover of X has an A-refinement.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-26.