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On Properties Characterizing Sequentially Compact Spaces
by
Ivan Gotchev
Department of Mathematics and Statistics, University of Maine, Orono, Maine, U.S.A.
A space X is called sequentially compact provided that every sequence in X has a convergent subsequence.
Sequentially compact spaces have been characterized in several ways (see J. E. Vaughan, Countable Compact and Sequentially Compact Spaces, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 569 - 602.) At the International Conference on Set-Theoretic Topology and its Applications (Ehime University, Matsuyama, Japan, 1994) the present author reported the following characterization of sequentially compact spaces.
A T1 space is sequentially compact if and only if every countable sequentially open cover has a finite subcover.
Based on this result we obtain new characterizations of sequentially compact spaces studying properties of the sequential topology of the original space.
Date received: July 1, 2000
Copyright © 2000 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 # caeh-58.