The Katětov Dimension of Proximity Spaces

H. L. Bentley, M. Hušek and R. G. Ori
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H. L. Bentley: University of Toledo, Department of Mathematics
M. Hušek: Charles University, Department of Mathematics
R. G. Ori: University of Durban-Westville, Department of Mathematics

A chapter in Categorical Topology, 1996, pp 43-55 from Springer

Abstract: Abstract An analogue of Katětov’s theorem on the equality between the dimension of a Tychonov space and the analytic dimension of its ring of bounded real-valued continuous maps is established for proximity spaces and proximally continuous maps by an internal method of proof. A new kind of filter, called proximally prime filter, arises naturally as a tool in this theory.

Keywords: proximity space; analytic subalgebra; proximally prime filter; dimension; 54F45; 54E05; 54C40 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_4

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DOI: 10.1007/978-94-009-0263-3_4

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