Measure-Theoretic Characterizations of Certain Topological Properties
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 99-109
MSC: Primary 28C15, 54D45, 54D99; Secondary 54E15, 54E50.
DOI: 10.4064/ba53-1-9
Abstract
It is shown that Čech completeness, ultracompleteness and local compactness can be defined 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.
