All cluster points of countable sets in supercompact spaces are the limits of nontrivial sequences

Yang, Zhong Qiang

doi:10.1090/S0002-9939-1994-1209102-0

All cluster points of countable sets in supercompact spaces are the limits of nontrivial sequences
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Proc. Amer. Math. Soc. 122 (1994), 591-595 Request permission

Abstract:

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 ${G_\delta }$-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.

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