Programming Second and Third Order Properties of Topological Spaces
by
Zoltan Balogh
Miami University

The theme of this talk is a method of building toplogical spaces that was used to obtain the following results.

Theorem 1. There is a paracompact, perfectly normal space whose every subset is an F_\sigma-set, yet the space is not sigma-discrete.

Theorem 2. There are hereditarily normal Dowker spaces of cardinality of the continuum.

Theorem 3. There is a hereditarily normal space with properties as required to prove Morita's Third Duality Conjecture.

Although the particulars of these constructions are very different, we will concentrate on the common technique that can be used to attack other problems.

Date received: April 12, 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 # caae-04.