Additions to some results of Erdös and Tarski
A DC-space (or space of dense constancies) is a Tychonoff space such that for each there is a family of open sets , the union of which is dense in , such that , restricted to each , 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 -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...
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