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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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On Perfectly Normal Compacta
by
H. Murat Tuncali
Nipissing University, North Bay, Ontario, Canada
Coauthors: D. Daniel, J. Nikiel, L.B. Treybig, E.D. Tymchatyn

Under extra set-theoretic conditions, many constructions of compact spaces yield a space which contains a large family of pairwise disjoint sets. We show that under the Souslin Hypothesis, each compact space of weight \omega1 contains an uncountable almost null-family of non-degenerate pairwise disjoint closed subsets. Moreover, if X is a locally connected continuum, this family can be chosen to consist of nondegenerate pairwise disjoint subcontinua. We give some applications of this result to perfectly normal compact spaces.

Date received: June 19, 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 Conferences Inc. Document # cait-49.