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Paul J. Szeptycki - Normality and property (a)

PAUL J. SZEPTYCKI, Ohio University
Normality and property (a)

A space X is said to have property (a) if for each open cover U and each dense $D \subseteq X$, there is a closed discrete $E \subseteq D$such that $st(E,U) = \bigcup \{u \in U:u \cap E \neg \emptyset\} = X$. This property was recently introduced by M. Matveev and is of particular interest when X is countably compact. Although not a priori obvious, property (a) is closely related to normality. I will discuss recent theorems, examples and open questions.


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