Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T19:59:39.893Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON SPACES WITH A RANK 3-DIAGONAL

Part of: Fairly general properties Spaces with richer structures

Published online by Cambridge University Press:  19 May 2014

WEI-FENG XUAN  and
WEI-XUE SHI
WEI-FENG XUAN*
Affiliation:
Department of Mathematics, Nanjing Audit University, Nanjing 210093, China email wfxuan@nau.edu.cn
WEI-XUE SHI
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, China email wxshi@nju.edu.cn
*
✉wfxuan@nau.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.

We prove that if $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}X$ is a space satisfying the discrete countable chain condition with a rank 3-diagonal then the cardinality of $X$ is at most $\mathfrak{c}$.

Keywords

cardinalityDCCCrank 3-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 90 , Issue 3 , December 2014 , pp. 521 - 524
Copyright
Copyright © 2014 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 (2006), 585–597.Google Scholar
Buzyakova, R. Z., ‘Cardinalities of ccc-spaces with regular G δ-diagonals’, Topology Appl. 153 (2006), 1696–1698.Google Scholar
Engelking, R., General Topology, Sigma Series in Pure Mathematics, 6 (Heldermann Verlag, Berlin, 1989).Google Scholar
Ginsburg, J. and Woods, R. G., ‘A cardinal inequality for topological spaces involving closed discrete sets’, Proc. Amer. Math. Soc. 64 (1977), 357–360.Google Scholar
Kunen, K. and Vaughan, J., Handbook of Set-Theoretic Topology (Elsevier, Amsterdam, 1984).Google Scholar
Shakhmatov, D. B., ‘No upper bound for cardinalities of Tychonoff CCC spaces with a G δ-diagonal exists’, Comment. Math. Univ. Carolin. 25 (1984), 731–746.Google Scholar
Uspenskij, V. V., ‘A large F σ-discrete Frechet space having the Souslin property’, Comment. Math. Univ. Carolin. 25 (1984), 257–260.Google Scholar
Wiscamb, M. R., ‘The discrete countable chain condition’, Proc. Amer. Math. Soc. 23 (1969), 608–612.CrossRefGoogle Scholar
Xuan, W. F. and Shi, W. X., ‘A note on spaces with rank 2-diagonal’, Bull. Aust. Math. Soc. , to appear; doi:10.1017/S0004972713001184.Google Scholar