Local properties of transitive quasi-uniform spaces

• Main Author: Seyedin, Massood
• Other Authors: Mathematics
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: LD5655.V856 1972.S48; Quasi-uniform spaces
• Online Access: http://hdl.handle.net/10919/38605; http://scholar.lib.vt.edu/theses/available/etd-06122010-020732/

If (X,Ƭ) is a topological space, then a quasi-uniformity U on X is compatible with Ƭ if the quasi-uniform topology, Ƭ_u = 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.