Diagonal Cauchy spaces

Publisher: Cambridge University Press

E-ISSN: 1755-1633|54|2|255-265

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.54, Iss.2, 1996-10, pp. : 255-265

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Abstract

A diagonal condition is defined which internally characterises those Cauchy spaces which have topological completions. The T2 diagonal Cauchy spaces allow both a finest and a coarsest T2 diagonal completion. The former is a completion functor, while the latter preserves uniformisability and has an extension property relative to θ-continuous maps.