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Algebras and spaces of dense constancies

Angelo BellaJorge MartinezScott D. Woodward — 2001

Czechoslovak Mathematical Journal

A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f C ( X ) there is a family of open sets { U i i I } , the union of which is dense in X , such that f , restricted to each U i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...

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