On p-pseudocompact spaces
by
Tamariz Mascarua Angel
Universidad Nacional Autónoma de México
Coauthors: Manuel Sanchis (Universitat Jaume I)

We prove some basic properties of p-bounded subsets (p in \omega^*) in terms of z-ultrafilters and families of continuous functions. We analyze the relations between p-pseudocompactness with other pseudocompact like-properties as p-compactness and \alpha-pseudocompactness where \alpha is a cardinal number. We give an example of a sequentially compact ultrapseudocompact \alpha-pseudocompact space which is not ultracompact, and we also give an example of an ultrapseudocompact totally countably compact \alpha-pseudocompact space which is not q-compact for any q in \omega^*, answering affirmatively to a question posed by S. García-Ferreira and Kocinac. We discuss the relation between p-pseudocompactness and p-compactness in normal and first countable spaces, and we prove that there exists an ultrapseudocompact topological group which is not p-compact for any p in \omega^*. We prove as well that \sigma-p-pseudocompactness and \sigma-pseudocompactness, and \sigma-p-compactness and \sigma-countable compactness are equivalent in the class of C_\pi-spaces. Finally, we characterize the spaces X for which C_\pi(X) is \sigma-\alpha-pseudocompact.

Date received: June 25, 1997

Copyright © 1997 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 # caao-25.