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Colloquium on Topology, Gyula, Hungary
August 9-15, 1998
János Bolyai Mathematical Society
Budapest, Hungary

Organizers
M. Bognár, A. Császár (chairman), J. Gerlits, I. Juhász, E. Makai, G. Moussong, R. Rimányi, L. Soukup, A. Stipsicz, J. Szenthe, A. Szücs (secretary)

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Generalized Closed Sets, Submaximal Spaces and Extremally Disconnected Spaces
by
Maximilian Ganster
Graz University of Technology
Coauthors: Jiling Cao, Ivan Reilly

A subset A of a topological space X is called generalized closed if [`A] subset or equal U whenever A subset or equal U and U is open (N. Levine, 1970). Recently there has been considerable interest in various forms of generalized closed sets whose definitions involve \alpha-open, semi-open and preopen sets. In this talk we will mainly discuss a diagram of J. Dontchev which exhibits the most important relationships between these many concepts. It will turn out that submaximal spaces and extremally disconnected spaces are strongly involved in this matter.
This talk covers joint work with Jiling Cao and Ivan Reilly.

Date received: May 6, 1998

Copyright © 1998 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 # cabc-08.