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

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Garrido, M. Isabel and Montalvo, Francisco (1994) Uniform density and m -density for subrings of C(X. Extracta Mathematicae, 9 (1). pp. 48-50. ISSN 0213-8743

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Official URL: http://dmle.cindoc.csic.es/pdf/EXTRACTAMATHEMATICAE_1994_09_01_07.pdf




Abstract

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


Item Type:Article
Uncontrolled Keywords:u-dense subring; m-dense
Subjects:Sciences > Mathematics > Topology
ID Code:21707
Deposited On:06 Jun 2013 16:12
Last Modified:19 Feb 2019 11:22

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