Product Property on Generalized Lindelof Spaces
by
Adem Kilicman
University Putra Malaysia
Coauthors: A. J. Fawakhrehf

Many of the results on the invariance of covering properties under the formation of a product are negative, in that covering properties are simply not preserved by products unless one or more of the factors are assumed to satisfy additional conditions. In this work, we discuss this matter in connection with generalizations of Lindelöf spaces, namely: nearly Lindelöf, almost Lindelöf and weakly Lindelöf spaces. We conclude that these topological properties are not preserved by products and we give some necessary conditions for these covering properties to be preserved under a finite product.

We also show that the product of a nearly Lindelöf weak P-space with a nearly Lindelöf space is nearly Lindelöf, and that the product of a Lindelöf P-space with a Lindelöf space is Lindelöf. Since a finite product of weak P-Spaces is a weak P-Space, we deduce that a finite product of nearly Lindelöf spaces is nearly Lindelöf. Moreover, the product of two almost Lindelöf spaces need not be almost Lindelöf, but the product of an almost Lindelöf space with a nearly compact space is almost Lindelöf. In this study, we also prove that the product of an almost Lindelöf weak P-Space with an almost Lindelöf space is almost Lindelöf, and finite products of almost Lindelöf spaces are almost Lindelöf.

We deduce further that the product of a weakly Lindelöf space with a nearly compact space is weakly Lindelöf.

Date received: May 28, 2001

Copyright © 2001 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 # cagx-08.