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Local properties of transitive quasi-uniform spaces

If (X,Ƭ) is a topological space, then a quasi-uniformity U on X is compatible with Ƭ if the quasi-uniform topology, Ƭ<sub>u</sub> = Ƭ. This paper is concerned with local properties of quasi-uniformities on a set X that are compatible with a given topology on X.

Chapter II is devoted to the construction of Hausdorff completions of transitive quasi-uniform spaces that are members of the Pervin quasi-proximity class.

Chapter III discusses locally complete, locally precompact, locally symmetric and locally transitive quasi-uniform spaces.

Chapter IV is devoted to function spaces of quasi-uniform spaces.

Chapter V and the Appendix are concerned with the topological homeomorphism groups of quasi-uniform spaces. / Ph. D.

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38605
Date12 June 2010
CreatorsSeyedin, Massood
ContributorsMathematics
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeDissertation, Text
Format64 leaves, BTD, application/pdf, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationOCLC# 22466742, LD5655.V856_1972.S48.pdf

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