Covering Properties and Metrisation of Manifolds*

David Gauld and M.K. Vamanamurthy


There are many conditions equivalent to metrisability for a topological manifold which are not equivalent to metrisability for topological spaces in general. What are the weakest such? We show that a number of weak covering properties which are equivalent to metrisability for a manifold, for example metaLindel"{o}f, may be further weakened by considering only covers of cardinality the first uncountable ordinal. Extensions to higher cardinals are discussed,

$[ heta, kappa]$-compact, linearly Lindel"{o}f, $omega_1$-Lindel"{o}f, $omega_1$-metaLindel"{o}f, metrisable, manifold, property pp.

Math Review Classification
Primary *2000 Mathematics Subject Classification: 03E75, 54D20, 54E35, 57N05, 57N15.

Last Updated
27 October 1999

10 pages

This article is available in: