Proceedings of the American Mathematical Society

Author(s): Zhongqiang Yang; Wei Sun
Journal: Proc. Amer. Math. Soc. 128 (2000), 1215-1219.
MSC (1991): Primary 54D30
Posted: August 3, 1999
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Abstract: A Hausdorff topological space is called supercompact if there exists a subbase such that every cover consisting of this subbase has a subcover consisting of two elements. In this paper, we prove that every non-P-point in any continuous image of a supercompact space is the limit of a nontrivial sequence. We also prove that every non-P-point in a closed $G_{\delta}$ -subspace of a supercompact space is a cluster point of a subset with cardinal number $\leq c.$ But we do not know whether this statement holds when replacing

by the countable cardinal number. As an application, we prove in ZFC that there exists a countable stratifiable space which has no supercompact compactification.

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Zhongqiang Yang
Affiliation: Department of Mathematics, Shaanxi Normal University, Xi'an, 710062, People's Republic of China
Email: yangmathsnuc@ihw.com.cn

Wei Sun
Affiliation: Xi'an Institute of Technology, Xi'an, 710032, People's Republic of China

DOI: 10.1090/S0002-9939-99-05119-9
PII: S 0002-9939(99)05119-9
Keywords: Supercompact, P-point, sequence, compactification
Received by editor(s): March 8, 1998
Received by editor(s) in revised form: May 20, 1998
Posted: August 3, 1999
Additional Notes: This work is supported by the National Education Committee of China for outstanding youths and by the National Education Committee of China for Scholars returning from abroad.
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

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