A. Bella, University of Messina, 98166 Messina, Italy, e-mail: bella@dipmat.unict.it; J. Martinez, University of Florida, Gainesville, FL 32611, USA, e-mail martinez@math.ufl.edu; S. Woodward, Lees-McRae University, Banner Elk, NC, USA, e-mail: woodwards@lmc.edu
Abstract: 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 $\{U_i i\in I\}$, 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 are dense), and it is shown that all metrizable spaces have this property.
Keywords: space and algebra of dense constancy, $c$-spectrum
Classification (MSC 2000): 54C05, 54G99, 06F25, 16S90
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