Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T14:32:38.980Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON SPACES WITH A STRONG RANK 1-DIAGONAL

Part of: Fairly general properties Spaces with richer structures

Published online by Cambridge University Press:  20 November 2013

WEI-FENG XUAN  and
WEI-XUE SHI
WEI-FENG XUAN*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China email [email protected]
*
✉[email protected]
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.

We mainly prove that, assuming $\mathfrak{b}= \mathfrak{c}$, every regular star-compact space with a strong rank 1-diagonal is metrisable.

Keywords

star-compactstrong rank 1-diagonal

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54E35: Metric spaces, metrizability
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 510 - 513
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Arhangel’skii, A. V. and Buzyakova, R. Z., ‘The rank of the diagonal and submetrizability’, Comment. Math. Univ. Carolin. 47 (4) (2006), 585–597.Google Scholar
Chaber, J., ‘Conditions which imply compactness in countably compact spaces’, Bull. Acad. Polon. Sci. Ser. Sci. Math. 24 (11) (1976), 993–998.Google Scholar
Engelking, R., General Topology, Sigma Series in Pure Mathematics 6 (Heldermann Verlag, Berlin, 1989).Google Scholar
Kunen, K. and Vaughan, J., Handbook of Set-theoretic Topology (Elsevier, Amsterdam, 1984).Google Scholar
Matveev, M. V., ‘A survey on star-covering properties’, Topology Atlas, Preprint no. 330 (1998).Google Scholar
Mrowka, S., ‘On completely regular spaces’, Fund. Math. 41 (1) (1955), 105–106.CrossRefGoogle Scholar
Sneider, V., ‘Continuous images of Souslin and Borel sets; Metrization theorems’, Dokl. Akad. Nauk SSSR 50 (1959), 77–79.Google Scholar
van Douwen, E. K., Reed, G. M. and Roscoe, A. W., ‘Star covering properties’, Topology Appl. 39 (1) (1991), 71–103.Google Scholar
Yang, E. and Shi, W., ‘An answer to van Mill’s question’, Bull. Aust. Math. Soc. 78 (2008), 353–355.Google Scholar