Quasi-pseudometrics over Tikhonov semifields and fixed point theorems

Author

Ronald Evans Satterwhite

Abstract

"It has been shown that topological spaces are characterized as quasi-pseudometric spaces over some Tikhonov semifield.

Sufficient conditions are given for a T₁ space to be metrizable over some Tikhonov semifield.

Completely regular (uniform) spaces are characterized as pseudornetric spaces over some Tikhonov semifield.

Certain metric, pseudornetric, quasi-metric, quasipseudometric spaces over a Tikhonov semifield are shown to be respectively metric, pseudometric, quasi-metric, quasipseudometric spaces in the usual sense.

Several results from fixed point theory in the metric space setting are generalized to the setting of completely regular (uniform) Hausdorff spaces."--Abstract, page ii.

Advisor(s)

Hicks, Troy L.

Committee Member(s)

Hatfield, Charles, 1920-1993
Haddock, Glen
Pursell, Lyle E.
Oakes, Robert A.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1972

Pagination

iv, 54 pages

Note about bibliography

Includes bibliographical references (pages 52-53).

Rights

© 1972 Ronald Evans Satterwhite, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Topological spacesMetric spacesHausdorff compactificationsFixed point theory

Thesis Number

T 2791

Print OCLC #

6037185

Electronic OCLC #

904151608

Recommended Citation

Satterwhite, Ronald Evans, "Quasi-pseudometrics over Tikhonov semifields and fixed point theorems" (1972). Doctoral Dissertations. 184.
https://scholarsmine.mst.edu/doctoral_dissertations/184