Doctoral Dissertations
Abstract
"Locally quasi-uniform spaces are studied, and it is shown that a topological space (X,t} admits exactly one compatible locally quasi-uniform structure if and only if tis finite.
A general topological result is given showing that a topological space with an infinite topology has either an infinite ascending or an infinite descending sequence of open sets.
The concept of aw-space is introduced, and it is ii shown that every w-space admits a strongly complete quasi-uniform structure. Also, a characterization of w-spaces is given showing when the fine quasi-uniform structure is equal to the fine locally quasi-uniform structure.
An example is given showing that not every topological space admits a strongly complete quasi-uniform structure"-- Abstract, p. ii
Advisor(s)
Hicks, Troy L.
Committee Member(s)
Haddock, Glen
Pursell, Lyle E., 1926-2015
Pyron, Howard D.
Illegible Signature
Department(s)
Mathematics and Statistics
Degree Name
Ph. D. in Mathematics
Publisher
University of Missouri--Rolla
Publication Date
1978
Pagination
iv, 38 pages
Note about bibliography
Includes bibliographical references (pages 36-37)
Rights
© 1978 Shirley Carpenter Huffman, All rights reserved.
Document Type
Dissertation - Open Access
File Type
text
Language
English
Thesis Number
T 4426
Print OCLC #
6009418
Recommended Citation
Huffman, Shirley Carpenter, "Locally quasi-uniform structures and strongly complete quasi-uniform structures" (1978). Doctoral Dissertations. 323.
https://scholarsmine.mst.edu/doctoral_dissertations/323
