Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-13T02:32:22.536Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Alas, O. T., Junqueira, L. R., Mill, J. van, Tkachuk, V. V. and Wilson, R. G., ‘On the extent of star countable spaces’, Cent. Eur. J. Math. 9(3) (2011), 603–615.CrossRefGoogle Scholar
[2]Alas, O. T., Junqueira, L. R. and Wilson, R. G., ‘Countability and star covering properties’, Topology Appl. 158 (2011), 620–626.CrossRefGoogle Scholar
[3]Engelking, R., General Topology, 2nd edn, Sigma Series in Mathematics, 6 (Heldermann, Berlin, 1989).Google Scholar
[4]Matveev, M. V., ‘A survey on star-covering properties’, Topological Atlas, Preprint No. 330, 1998.Google Scholar
[5]Noble, N., ‘Countably compact and pseudocompact products’, Czechoslovak Math. J. 279(4) (1985), 825–829.Google Scholar
[6]Shahmatov, D. B., ‘On pseudocompact spaces with point base’, Dokl. Akad. Nauk SSSR 19 (1969), 390–397.Google Scholar
[7]Song, Y., ‘On σ-starcompact spaces’, Appl. Gen. Topol. 9(2) (2008), 293–299.CrossRefGoogle Scholar
[8]Douwen, E. K. van, Reed, G. K., Roscoe, A. W. and Tree, I. J., ‘Star covering properties’, Topology Appl. 39 (1991), 71–103.CrossRefGoogle Scholar
[9]Mill, J. van, Tkachuk, V. V. and Wilson, R. G., ‘Classes defined by stars and neighbourhood assignments’, Topology Appl. 154 (2007), 2127–2134.CrossRefGoogle Scholar