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 -subspace of a supercompact space is a cluster point of a subset with cardinal number 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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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

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