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DOMINATION CONDITIONS UNDER WHICH A COMPACT SPACE IS METRISABLE

Part of: Set theory Basic constructions Fairly general properties Spaces with richer structures

Published online by Cambridge University Press:  11 February 2015

ALAN DOW  and
DAVID GUERRERO SÁNCHEZ
ALAN DOW
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, NC, USA
DAVID GUERRERO SÁNCHEZ*
Affiliation:
Instituto de Matemática e Estadística, Universidade de São Paulo, Brazil email dgs@ciencias.unam.mx
*
✉dgs@ciencias.unam.mx
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Abstract

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In this note we partially answer a question of Cascales, Orihuela and Tkachuk [‘Domination by second countable spaces and Lindelöf ${\rm\Sigma}$-property’, Topology Appl.158(2) (2011), 204–214] by proving that under $CH$ a compact space $X$ is metrisable provided $X^{2}\setminus {\rm\Delta}$ can be covered by a family of compact sets $\{K_{f}:f\in {\it\omega}^{{\it\omega}}\}$ such that $K_{f}\subset K_{h}$ whenever $f\leq h$ coordinatewise.

Keywords

compact spaceℙ-dominated spacesmall diagonal

MSC classification

Primary: 54E35: Metric spaces, metrizability
Secondary: 03E50: Continuum hypothesis and Martin's axiom 54B10: Product spaces 54D30: Compactness
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 502 - 507
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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