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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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C-metacompact Spaces
by
E. M. Grabner
Slippery Rock University
Coauthors: G. C. Grabner

Suppose that X is a topological space and C subset or equal X. We say that X is C-metacompact provided every open cover V of X has an open refinement U such that Ux={U in U:x in U} is finite for all x in C. We investigate basic properties of this class of spaces and relate C-metacompactness to relative topological properties introduced by A. Arkhangel'skii and I. Gordienko.

Suppose that C subset or equal X is closed in the space X. Then X is C-metacompact if and only if C is metacompact.

Suppose f:X --> Y is a closed mapping onto Y and C is a closed subset of X. If X is C-metacompact then Y is f(C)-metacompact.

Suppose C is a subset of a space X. The space X is C-metacompact if and only if every directed open cover U has an open refinement that is point finite on D.

Date received: June 26, 1997

Copyright © 1997 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 # caao-27.