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Uniform density and M−density for subrings of C(X)

Published online by Cambridge University Press:  17 April 2009

M.I. Garrido  and
F. Montalvo
M.I. Garrido
Affiliation:
Departamento de MatemáticasUniversidad de ExtremaduraAvda. de Elvas s/n. 06071 Badajoz, Spain
F. Montalvo
Affiliation:
Departamento de MatemáticasUniversidad de ExtremaduraAvda. de Elvas s/n. 06071 Badajoz, Spain
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This paper deals with the equivalence between u−density and m−density for the subrings of C(X). It was proved by Kurzweil that such equivalence holds for those subrings that are closed under bounded inversion. Here an example is given in C(N) of a u−dense subring that is not m−dense. It is deduced that the two types of density coincide only in the trivial case where these topologies are the same, that is, if and only if X is a pseudocompact space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 427 - 432
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, F.W., ‘Approximation in systems of real-valued continuous functions’, Trans. Amer. Math. Soc. 103 (1962), 249–271.CrossRefGoogle Scholar
[2]Garrido, M.I. and Montalvo, F., ‘On uniformly dense and m−dense subsets of C(X)’, Extracta Math. 6 (1991), 15–16.Google Scholar
[3]Garrido, M.I. and Montalvo, F., ‘Uniform approximation theorems for real-valued continuous functions’, Topology Appl. 45 (1992), 145–155.CrossRefGoogle Scholar
[4]Gillman, L. and Jerison, M., Rings of continuous functions (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[5]Hewitt, E., ‘Rings of real-valued continuous functions. I’, Trans. Amer. Math. Soc. 64 (1948), 45–99.Google Scholar
[6]Kurzweil, J., ‘On approximation in real Banach spaces’, Studia Math. 14 (1954), 214–231.Google Scholar