Realcompact Alexandroff spaces and regular σ-frames
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University of Cape Town
In the early 1940's, A.D. Alexandroff [1940), [1941) and  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.
Bibliography: pages 96-103.
Gilmour, C. 1981. Realcompact Alexandroff spaces and regular σ-frames. University of Cape Town.