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Measure-theoretic characterizations of certain topological properties

Buhagiar D., Chetcuti E., Dvurečenskij A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 1

99-109

It is shown that Cech completeness, ultracompleteness and local compactness can be denned by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.