Advanced Search

A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C\left(X\right)$ there is a family of open sets $\{U_{i}i\in I\}$, 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...