Article contents
DOMINATION CONDITIONS UNDER WHICH A COMPACT SPACE IS METRISABLE
Published online by Cambridge University Press: 11 February 2015
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
References
- 5
- Cited by