Characterizing topologies by classes of functions and multifunctions

"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.

Name thesis:degree_name

Ph. D. in Mathematics

Grantor

University of Missouri--Rolla

Year dc:date.available

2016

Author dc:creator

• Cramer, Alexander Hamlin

• Mathematics

Repository record dc:identifier

https://scholarsmine.mst.edu/doctoral_dissertations/1841

OAI identifier oai:identifier

oai:scholarsmine.mst.edu:doctoral_dissertations-2843