Atlas home || Conferences | Abstracts | about Atlas

Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

View Abstracts
Conference Homepage

Strongly Hewitt spaces and applications to spaces C(X)
by
Jerzy Kakol
A. Mickiewicz University, Poznan
Coauthors: W. Sliwa (A. Mickiewicz University of Poznan)

We study completely regular spaces X (under the name strongly Hewitt) such that for any sequence (xn) in the remainder of the Stone-Cech compactification of X there exists a real continuous function on the Stone-Cech compactification which is positive on X and vanishes on some subsequence of (xn). It is proved that X is strongly Hewitt iff it is Hewitt and the remainder is countably compact. Every strongly Hewitt space of pointwise countable type is locally compact. Results of Baumgartner and Douwen are extended. Applications to spaces C(X) of real continuous functions on X endowed with the compact-open topology are included. Among other things, it is proved that whenever X is of pointwise countable type then C(X) is bornological and Baire-like (in the sense of Saxon) iff X is strongly Hewitt. Nevertheless, we provide examples of locally compact strongly Hewitt spaces X for which C(X) is not a Baire space.

(T)

Date received: November 23, 1999

Copyright © 1999 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 # cado-31.