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Uniform density and m-density for subrings of C(X)

Garrido Carballo, M. Isabel and Montalvo, Francisco (1994) Uniform density and m-density for subrings of C(X). Bulletin of the Australian Mathematical Society, 49 (3). pp. 427-432. ISSN 0004-9727

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:U-density; m-density
Subjects:Sciences > Mathematics > Topology
ID Code:15537
References:

F.W. Anderson, 'Approximation in systems of real-valued continuous functions', Trans.Amer. Math. Soc. 103 (1962), 249-271.

M.I. Garrido and F. Montalvo, 'On uniformly dense and m-dense subsets of C(X)\Extracta Math. 6 (1991), 15-16.

M.I. Garrido and F. Montalvo, 'Uniform approximation theorems for real-valued continuous functions', Topology Appl. 45 (1992), 145-155.

L. Gillman and M. Jerison, Rings of continuous functions (Springer-Verlag, Berlin, Heidelberg,New York, 1976).

E. Hewitt, 'Rings of real-valued continuous functions. I', Trans. Amer. Math. Soc. 64 (1948), 45-99.

J. Kurzweil, 'On approximation in real Banach spaces', Studia Math. 14 (1954), 214-231.

Deposited On:08 Jun 2012 09:15
Last Modified:06 Feb 2014 10:26

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