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A NOTE ON SPACES WITH RANK 2-DIAGONAL

Part of: Spaces with richer structures Fairly general properties

Published online by Cambridge University Press:  02 April 2014

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

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We prove that if a space $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}X$ with a rank 2-diagonal either has the countable chain condition or is star countable then the cardinality of $X$ is at most $\mathfrak{c}$.

Keywords

star countablecccrank 2-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 1 , August 2014 , pp. 141 - 143
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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