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All Cluster Points of Countable Sets in Supercompact Spaces are the Limits of Nontrivial Sequences
Proceedings of the American Mathematical Society
Vol. 122, No. 2 (Oct., 1994), pp. 591-595
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2161053
Page Count: 5
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A space is called supercompact if it has an open subbase such that every cover consisting of elements of the subbase has a subcover consisting of two elements. In this paper we prove that, in a continuous image of a closed Gδ-set of a supercompact space, a point is a cluster point of a countable set if and only if it is the limit of a nontrivial sequence. As corollaries, we answer questions asked by J. van Mill et al.
Proceedings of the American Mathematical Society © 1994 American Mathematical Society