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On a theorem for $M$-spaces

1967
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Proceedings of the Japan Academy
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1. Introduction. Prof. K. Morita [4 has introduced the notion of M-spaces. He calls a topological space X an M-space if there exists a normal sequence {1I i-1, 2, ...} of open coverings of X satisfying the condition (.) below: (If a family consisting of a countable number of subsets Jof X has the finite intersection property and contains as a (*) member a subset of S(x0, 1I) for every i and for some fixed point x0 of X, then {/ K } =/= . Recently, T. Kand5 2J has proved the following theorem.

doi:10.3792/pja/1195521518
fatcat:rmlvipfg3jcovks746kgz46oqy