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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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Iterated Starcompact Topological Spaces
by
Junhui Kim
Ehime University, Japan

Starcovering properties were studied systematically in [1]. The following is a generalization of n-starcompactness defined in [1]. We shall call it iterated starcompact property.

Definition [2] A space X is said to be (n, k)-starcompact if for every open cover U of X there is an n-starcompact subspace A of X such that stk(A, U)=X.

We discuss iterated starcompact properties which are located between countable compactness and pseudocompactness, and consider counterexamples and relationships among them.

[1] E. van Douwen, G. Reed, A. Roscoe and I. Tree, Star covering properties, Topology Appl. , 39 (1991), 71-103.

[2] M. Matveev, A survey on star covering properties, Topology Atlas , Preprint No. 330, 1998.

Date received: June 20, 2002

Copyright © 2002 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 Mathematical Conference Abstracts. Document # cait-54.