Sequential Spaces and Cleavability
by
Ljubiša D.R. Kočinac

We consider relationships between cleavability and p-sequential-like properties of topological spaces, p in \beta\omega\\omega.

1. If a compact space X is cleavable over the class K of ccc p-sequential spaces, then X is an FU(q)-space for some q in \beta\omega\\omega.
2. If a separable p-compact space X is cleavable over the class of p-closed spaces, then X is p-sequential and an FU(q)-space for some q in \beta\omega\\omega.
3. If a countably compact Tychonoff space X is closed pointwise cleavable over the class of Fréchet-Urysohn spaces, then X is \omega-bounded.

   We give an easy proof of the following result.

4. If a (ultra)compact space X is cleavable over the class of all sequential spaces, then X is also sequential.

Date received: June 24, 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 # caah-54.