Doctoral Dissertations


"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T1 space does not necessarily have a T1 strong completion.

The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.

Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.

A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure"--Abstract, page iii.


Hicks, Troy L.

Committee Member(s)

Haddock, Glen
Rakestraw, Roy M.
Rigler, A. K.
Stanojevic, Caslav V., 1928-2008


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


University of Missouri--Rolla

Publication Date



iv, 33 pages

Note about bibliography

Includes bibliographical references (page 32).


© 1973 Karen Sylvia Carter, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type




Library of Congress Subject Headings

Quasi-uniform spaces

Thesis Number

T 2784

Print OCLC #


Electronic OCLC #


Link to Catalog Record

Electronic access to the full-text of this document is restricted to Missouri S&T users. Otherwise, request this publication directly from Missouri S&T Library or contact your local library.

Share My Dissertation If you are the author of this work and would like to grant permission to make it openly accessible to all, please click the button above.