%0 Journal Article
%A Garrido, M. Isabel
%A Montalvo, Francisco
%T Uniform density and m -density for subrings of C(X
%D 1994
%@ 0213-8743
%U https://hdl.handle.net/20.500.14352/58544
%X Let C(X)  denote the continuous real-valued functions on a topological space X . The question of whether a u -dense subring of C(X)  is m -dense is studied in this note. Recall that neighborhoods of a function f  in the u -topology are determined by an interval (f−ε,f+ε)  for ε  a positive number and in the m -topology by intervals (f−e,f+e)  for u  a positive unit in C(X) . J. Kurzweil [Studia Math. 14 (1954), 214–231, had shown that u -denseness and m -denseness are equivalent for subrings of C(X)  closed under bounded inversion. Here, the authors prove that this result is not valid for arbitrary subrings of C(X) . In particular, they show that the property of every u -dense subring being m -dense is equivalent to X  being pseudocompact
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