A weak normality property
by
William G. Fleissner
University of Kansas

We say that a space X has Property N if whenever C and D are disjoint closed sets, then there is an open set U covering C such that if C subset K subset U and K is closed in X \D, then cl_XK \cap D = \emptyset. Easy results: 1. Normality implies property N. 2. Property N + Frechet-Urysohn + T₂ implies normality. If there is a T₃, regular, not normal space with property N, then there is a T₂, not regular space with property N. A not easy result due to LeDonne: There is a T₂, not regular space with property N. Open question: Is there a T₃, regular, not normal space with property N? A plausible place to seek such a space is \omega^*\{p} or \kappa^* \{p}.

Date received: February 28, 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 # caam-33.