Abstract:
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,