View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Missouri University of Science and Technology (Missouri S&T): Scholars' Mine Scholars' Mine Doctoral Dissertations Student Theses and Dissertations 1970 Completeness and related topics in a quasi-uniform space John Warnock Carlson Follow this and additional works at: https://scholarsmine.mst.edu/doctoral_dissertations Part of the Mathematics Commons Department: Mathematics and Statistics Recommended Citation Carlson, John Warnock, "Completeness and related topics in a quasi-uniform space" (1970). Doctoral Dissertations. 2144. https://scholarsmine.mst.edu/doctoral_dissertations/2144 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact
[email protected]. COMPLETENESS AND RELATED TOPICS IN A QUASI-UNIFORM SPACE by JOHN WARNOCK CARLSON, 1940 - A DISSERTATION Presented to the Faculty of the Graduate School of the UNIVERSITY OF MISSOURI - ROLLA In Partial Fulfillment of the Requirements for t h e Degree DOCTOR OF PHILOSOPHY in MATHEMATICS 1970 ii ABSTRACT Completions and a strong completion of a quasi- uniform space are constructed and examined. It is shown that the trivial completion of a To space is T 0 • Ex amples are given to show that a T 1 space need not have a T 1 strong completion and a T 2 space need not have a T 2 completion. The nontrivial completion constructed is shown to be T 1 if the space is T 1 and the quasi-uniform structure is the Pervin structure.