In [5], Zenor stated the definition of weakly normal. In the main, since weak normality does not imply either normality or regularity, various properties related to either normality or regularity will be considered in the context of weak normality.Throughout this paper the word “space” will mean topological space. The closure of a point set M will be denoted by cl(M). The closure of a point set M with respect to the subspace K will be denoted by cl(M, K). Definition 1. A space S is weakly normal provided that if is a monotonically decreasing sequence of closed sets in S with no common part and H is a closed set in S not intersecting H 1, then there is a positive integer N and an open set D such that HN ⊂ D and cl(D) does not intersect H.
Ball, Eugene S. Weak Normality and Related Properties. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 997-1001. doi: 10.4153/CJM-1970-114-6
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title = {Weak {Normality} and {Related} {Properties}},
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url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-114-6/}
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