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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

All non-P-points are the limits of nontrivial sequences in supercompact spaces


Authors: Zhongqiang Yang and Wei Sun
Journal: Proc. Amer. Math. Soc. 128 (2000), 1215-1219
MSC (1991): Primary 54D30
Published electronically: August 3, 1999
MathSciNet review: 1637456
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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 $c$ 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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Additional Information

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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society