Some results on quasi-uniform spaces

Author

Karen Sylvia Carter

Abstract

"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.

Advisor(s)

Hicks, Troy L.

Committee Member(s)

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

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1973

Pagination

iv, 33 pages

Note about bibliography

Includes bibliographical references (page 32).

Rights

© 1973 Karen Sylvia Carter, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Quasi-uniform spaces

Thesis Number

T 2784

Print OCLC #

6036936

Electronic OCLC #

913469184

Recommended Citation

Carter, Karen Sylvia, "Some results on quasi-uniform spaces" (1973). Doctoral Dissertations. 191.
https://scholarsmine.mst.edu/doctoral_dissertations/191