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Compactness and Strong Separation

Published online by Cambridge University Press:  20 November 2018

David E. Cook
David E. Cook*
Affiliation:
University of Mississippi, University, Mississippi
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Two point sets H and K are said to be strongly separated if there exist two mutually exclusive domains DH and DK containing H and K respectively such that either and are mutually exclusive or · is R. L. Moore has shown [2, Theorem 153, Chapter I] that if S is a normal Moore space and H and K are two mutually separated point sets then H and K are strongly separated. In this paper it is shown that if 5 is a Moore space, (1) H and K are two mutually separated point sets and (2) the closure of the set of all boundary points of H which do not belong to is compact, then H and K are strongly separated.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 225 - 232
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Cook, David E., A conditionally compact point set with non-compact closure, Pacific J. Math. 35 (1970), 313–319.Google Scholar
2. Moore, R. L., Foundations of point set theory, Amer. Math. Soc. Colloq. Publ. Vol. 13, rev. ed. (Providence, R.I., 1962).Google Scholar
3. Whyburn, G. T., Analytical topology, Amer. Math. Soc. Colloq. Publ. Vol. 28, rev. ed. (Providence, R.I., 1963).Google Scholar