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A PSEUDOCOMPACT TYCHONOFF SPACE THAT IS NOT STAR LINDELÖF

Part of: Generalities

Published online by Cambridge University Press:  21 July 2011

YANKUI SONG
YANKUI SONG*
Affiliation:
Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210046, PR China (email: songyankui@njnu.edu.cn)
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Abstract

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Let P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X, there exists a subspace A⊆X with property P such that X=St(A,𝒰), where St(A,𝒰)=⋃ {U∈𝒰:U∩A≠0̸}. In this paper we construct an example of a pseudocompact Tychonoff space that is not star Lindelöf, which gives a negative answer to Alas et al. [‘Countability and star covering properties’, Topology Appl.158 (2011), 620–626, Question 3].

Keywords

pseudocompactstar countablestar σ-compactstar Lindelöf

MSC classification

Secondary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 452 - 454
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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