Realcompact Alexandroff spaces and regular σ-frames

In the early 1940's, A.D. Alexandroff [1940), [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals on these systems of functions and the additive set functions defined on the space. The Alexandroff spaces of this thesis are what Alexandroff himself called the completely normal spaces and what H. Gordon [1971) called the zero-set spaces.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1981

Author dc:creator

• Gilmour, Christopher Robert Anderson

Advisor dc:contributor.advisor

• Brümmer, Guillaume C L

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/21395

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/21395