Doctoral Dissertations

Abstract

"Various topological spaces are examined in an effort to describe topological spaces from a knowledge of their class of continuous selfmaps or their class of autohomeomorphisms. Relationships between topologies and their continuous selfmaps are considered. Several examples of topological spaces are given and their corresponding classes of continuous selfmaps are described completely. The problem, given a set X and a topology U when does there exist a topology V either weaker or stronger than U such that the class of continuous selfmaps of (X,V) contains the class of continuous selfmaps of (X,U), is considered. M* and S** spaces are defined and some their properties are considered. Two M* (or S**) spaces are shown to be homeomorphic if and only if certain semigroups of continuous selfmaps are isomorphic"--Abstract, page ii.

Advisor(s)

Haddock, Glen

Committee Member(s)

Penico, Anthony J., 1923-2011
Gillett, Billy E.
Hicks, Troy L.
Bertnolli, Edward C.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1969

Pagination

iv, 74 pages.

Note about bibliography

Includes bibliographical references (pages 72-73).

Rights

© 1969 Derald David Rothmann, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Topological spaces
Homeomorphisms
Topological dynamics
Mathematical analysis

Thesis Number

T 2361

Print OCLC #

6019790

Electronic OCLC #

854555238

Included in

Mathematics Commons

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