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A NOTE ON SPACES WITH A RANK 3-DIAGONAL

Part of: Spaces with richer structures Fairly general properties

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

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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

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