Doctoral Dissertations

Abstract

"Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T₀ space is T₀ . Examples are given to show that a T₁ space need not have a T₁ strong completion and a T₂ space need not have a T₂ completion. The nontrivial completion constructed is shown to be T₁ if the space is T₁ and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples are provided concerning properties which hold in a uniform space but do not hold in a quasi-uniform space. It is shown that if each member of a quasi-uniform structure is a neighborhood of the diagonal then the topology is uniformizable"--Abstract, page ii.

Advisor(s)

Hicks, Troy L.

Committee Member(s)

Haddock, Glen
Pursell, Lyle, E.
Gillett, Billy E.
Waggoner, Raymond C.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1970

Pagination

iv, 57 pages.

Note about bibliography

Includes bibliographical references (pages 55-56).

Rights

© 1970 John Warnock Carlson, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Quasi-uniform spaces
Completeness theorem

Thesis Number

T 2384

Print OCLC #

6020293

Electronic OCLC #

854624415

Included in

Mathematics Commons

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