Non-b-points in Compact Hausdorff Spaces
by
Andrzej Szymanski
Slippery Rock University

A point p ∈ X for which there are two closed subsets E, F of X such that {p} = cl(F-{p}) ∩cl(E-{p}) is called a b-point. Points that are not b-points are called non-b-points. We discuss properties and the existence of non b-points in compact Hausdorff spaces. We show that if p is a non-b-point in a compact Hausdorff space X, then for each open cover P of X-{p} there exists q ∈ X such that St(P, q) ∪{p} is an open neighborhood of p. The proof of this property utilizes the topological version of Fodor's Pressing Down Lemma.

Date received: February 27, 2008