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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38605 |
| Date | 12 June 2010 |
| Creators | Seyedin, Massood |
| Contributors | Mathematics |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | 64 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 22466742, LD5655.V856_1972.S48.pdf |
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