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
Subject Headings
Topological spaces
Homeomorphisms
Topological dynamics
Mathematical analysis
Thesis Number
T 2361
Print OCLC #
6019790
Electronic OCLC #
854555238
Link to Catalog Record
Recommended Citation
Rothmann, Derald David, "Characterizing topologies by continuous selfmaps" (1969). Doctoral Dissertations. 2143.
https://scholarsmine.mst.edu/doctoral_dissertations/2143