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Weak Normality and Related Properties

Published online by Cambridge University Press:  20 November 2018

Eugene S. Ball
Eugene S. Ball*
Affiliation:
Auburn University, Auburn, Alabama Tennessee Technological University, Cookeville, Tennessee
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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 H1, then there is a positive integer N and an open set D such that HN ⊂ D and cl(D) does not intersect H.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 997 - 1001
Copyright
Copyright © Canadian Mathematical Society 1970

References

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3. Ishikawa, T., On countably paracompact space, Proc. Japan Acad. 31 (1955), 686–687.Google Scholar
4. Moore, R. L., Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., No. 13 (Amer. Mfrth. Soc, Providence, R.I. (New York), 1932).Google Scholar
5. Zenor, P., On Countable paracompactness and normality, Prace Mat. 13 (1969), 23–32.Google Scholar