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March 2004 On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity
J.C. Ferrando, J. Kakol, M. López-Pellicer
Bull. Belg. Math. Soc. Simon Stevin 11(1): 127-132 (March 2004). DOI: 10.36045/bbms/1080056165

Abstract

Let $C_{0}\left( \Omega ,X\right)$ be the linear space of all continuous functions from a locally compact normal space $\Omega $ into a normed space $X$ vanishing at infinity, equipped with the supremum-norm topology. The main result of the paper says that if $X$ is barrelled, then the space $C_{0}\left( \Omega ,X\right) $ is always barrelled. This answers a question posed by J. Horváth.

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J.C. Ferrando. J. Kakol. M. López-Pellicer. "On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity." Bull. Belg. Math. Soc. Simon Stevin 11 (1) 127 - 132, March 2004. https://doi.org/10.36045/bbms/1080056165

Information

Published: March 2004
First available in Project Euclid: 23 March 2004

zbMATH: 1077.46031
MathSciNet: MR2059181
Digital Object Identifier: 10.36045/bbms/1080056165

Subjects:
Primary: 46A08 , 46B25

Keywords: $C_{0}\left(\Omega,X\right)$ spaces , barrelled space

Rights: Copyright © 2004 The Belgian Mathematical Society

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Vol.11 • No. 1 • March 2004
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