Sums, Products and Mappings of Weakly Pseudocmopact Spaces
by
Fred Eckertson
Univ Nacional Autonoma de Mexico

It is well-known that X is pseudocompact iff X is G_\delta-dense in \betaX. Generalizing pseudocompactness, García-Ferreira and García-Máynez have defined X to be weakly pseudocompact (w\psic) if X is G_\delta-dense in some compactification. Generally, the unwieldy nature of lattices of compactifications make it difficult to show spaces are not w\psic except in trivial cases. We present techniques to overcome this hurdle and show the property is misbehaved with respect to some rather nice mappings. We also address some questions posed by the originators and subsequent authors. In particular, there is a not pseudocompact space in which each z-set is w\psic, and a space is w\psic if its product with a not crowded Lindelöf space is w\psic or if it has an isolated point and its square is w\psic.

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-17.