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

Author:
Zhong Qiang Yang

Journal:
Proc. Amer. Math. Soc. **122** (1994), 591-595

MSC:
Primary 54D30

MathSciNet review:
1209102

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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 -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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209102-0

Keywords:
Supercompact,
limit,
sequence

Article copyright:
© Copyright 1994
American Mathematical Society