Abstract
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 are dense), and it is shown that all metrizable spaces have this property.
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Bella, A., Martinez, J. & Woodward, S.D. Algebras and Spaces of Dense Constancies. Czechoslovak Mathematical Journal 51, 449–461 (2001). https://doi.org/10.1023/A:1013767502518
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DOI: https://doi.org/10.1023/A:1013767502518