Compactness and Strong Separation
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 225-232
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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.
Cook, David E. Compactness and Strong Separation. Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 225-232. doi: 10.4153/CJM-1973-022-3
@article{10_4153_CJM_1973_022_3,
author = {Cook, David E.},
title = {Compactness and {Strong} {Separation}},
journal = {Canadian journal of mathematics},
pages = {225--232},
year = {1973},
volume = {25},
number = {2},
doi = {10.4153/CJM-1973-022-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-022-3/}
}
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[3] 3. Whyburn, G. T., Analytical topology, Amer. Math. Soc. Colloq. Publ. Vol. 28, rev. ed. (Providence, R.I., 1963). Google Scholar
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