First-Countability and the Fréchet-Urysohn Property of Hyperspace Topologies
by
Paolo Vitolo
Università della Basilicata
Coauthors: C. Costantini (Università della Basilicata)

We investigate the first-countability and the Fréchet-Urysohn property of the cocompact topology, on the collection of the closed subsets of a Hausdorff space X. In particular, we show that the cocompact topology is first-countable if and only if the space X is hereditarily Lindelöf and hemicompact; moreover, if X is first-countable, such a characterization holds as well for the Fréchet-Urysohn property.

Some similar results concerning other hyperspace topologies are established, too.

Date received: May 31, 1996

Copyright © 1996 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 # caag-06.