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Some Results on Quasi-Uniform Spaces

Published online by Cambridge University Press:  20 November 2018

Karen S. Carter  and
T. L. Hicks
Karen S. Carter
Affiliation:
Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A.
T. L. Hicks
Affiliation:
Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A.
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Constructions are made of a T1 space which does not have a T1 completion and of a quasi-uniform space which is complete, but not strongly complete. An example relating to a completion due to Popa is given. An alternate definition for Cauchy filter, called C-filter, is examined and a construction of a C-completion is given. We discuss quasi-pseudometrics over a Tikhonov semifield RΔ. Every topological space is quasi-pseudometrizable over a suitable RΔ. It is shown that if a quasi-pseudometric space over RΔ is complete, the corresponding quasi-uniform structure is C-complete. A general method for constructing compatible quasiuniform structures is given.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 39 - 51
Copyright
Copyright © Canadian Mathematical Society 1976

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