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, |
Keywords
$[ heta, kappa]$-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
Length
10 pages
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