Characterizing topologies by classes of functions and multifunctions

Author

Alexander Hamlin Cramer

Abstract

"Topological spaces are characterized by the algebraic and topological structures of their classes of continuous selfmaps. The problem of determining the topology of a set given certain classes of multifunctions or relations is considered. The algebraic structure of the upper semicontinuous multifunctions is shown to determine the topology of T₁ spaces. A partial order for classes of topologies for the real numbers is defined and relationships between various classes are established"--Abstract, page ii.

Advisor(s)

Haddock, Glen

Committee Member(s)

Bain, Lee J., 1939-
Hicks, Troy L.
Penico, Anthony J., 1923-2011
Pursell, Lyle E.
Rigler, A. K.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1971

Pagination

v, 56 pages

Note about bibliography

Includes bibliographical references (pages 54-55).

Rights

© 1971 Alexander Hamlin Cramer, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Topological spacesFunctionsTopological algebras

Thesis Number

T 2604

Print OCLC #

6037828

Electronic OCLC #

875561108

Recommended Citation

Cramer, Alexander Hamlin, "Characterizing topologies by classes of functions and multifunctions" (1971). Doctoral Dissertations. 1841.
https://scholarsmine.mst.edu/doctoral_dissertations/1841