On strong \tau-pseudocompactness, Preliminary Report
by
Jerry Vaughan
UNC-Greensboro

A space is strongly \tau-pseudocompact provided every continuous function from X into R^\tau is a closed mapping (A. V. Arhangel'skii, 1999). We give an internal characterization of strong \tau-pseudocompactness, and generalize Arhangel'skii's theorem which says that in any strongly \tau-pseudocompact space every closed subset with net weight at most \tau is compact. The internal characterization also may be used to give different proofs of several theorems of Arhangel'skii which together provide an internal proof of Arhangel'skii's theorem that says: If X is strongly 2^\tau-pseudocompact and t(X) <= \tau, then X is compact. By ``internal proof" we mean without directly using mappings into R^\tau or Stone-Cech compactifications.

Date received: May 29, 2003