On a preservation of completeness of uniform spaces by the functor PscT

It is shown that the functor P scT of t -additive probability measures does not preserve completeness of uniform spaces. Namely, P T( R c) is not complete. On the other hand, assuming Martin's Axiom, P scT ( X) is complete for every complete uniform space X of uniform weight < c.

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Bibliographic Details
Published in:Topology and its applications 1999, Vol.91 (1), p.25-45
Main Author: Fedorchuk, V.V.
Format: Article
Language:English
Subjects:
[formula omitted]-additive measure
Completeness
Functor
Martin's axiom
Probability measure
Pseudometric
Radon measure
Uniform space
Uniform weight
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Summary:It is shown that the functor P scT of t -additive probability measures does not preserve completeness of uniform spaces. Namely, P T( R c) is not complete. On the other hand, assuming Martin's Axiom, P scT ( X) is complete for every complete uniform space X of uniform weight < c.
ISSN:0166-8641
1879-3207
DOI:10.1016/S0166-8641(97)00240-X