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DOMINATION CONDITIONS UNDER WHICH A COMPACT SPACE IS METRISABLE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 3 / June 2015
- Published online by Cambridge University Press:
- 11 February 2015, pp. 502-507
- Print publication:
- June 2015
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- Article
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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.
