Geodesic
Algebras and spaces of dense constancies
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 449-461

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, 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.
Classification : 06F25, 16S90, 54C05, 54C35, 54G99
Keywords: space and algebra of dense constancy; $c$-spectrum 
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Bella, A.; Martinez, J.; Woodward, S. D. Algebras and spaces of dense constancies. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 449-461. http://geodesic.mathdoc.fr/item/CMJ_2001__51_3_a0/