AP-spaces and their applications
by
Vladimir Tkachuk
Universidad Autonoma Metropolitana de Mexico
Coauthors: I.V. Yaschenko

Given a topological space X and F subset X, say that F is almost closed if [`F]\F is a one-point set. If F is almost closed and [`F]\F={x}, we write F --> x. A space X is called AP-space if, for any A subset X and any x in [`A]\A, there is an almost closed F subset A such that F --> x. The space X is called WAP-space if, for any non-closed A subset X, there is an x in [`A]\A such that F --> x for some almost closed F subset A. We prove that any scattered space is hereditarily WAP and construct an example of a WAP-space which is not hereditarily WAP. Some applications of AP-spaces in C_p-theory are given.

Date received: January 31, 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 # cafw-14.