## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 1 (2004), 127-132.

Dates
First available in Project Euclid: 23 March 2004

https://projecteuclid.org/euclid.bbms/1080056165

Digital Object Identifier
doi:10.36045/bbms/1080056165

Mathematical Reviews number (MathSciNet)
MR2059181

Zentralblatt MATH identifier
1077.46031

#### Citation

Ferrando, J.C.; Kakol, J.; López-Pellicer, M. On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity. Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 1, 127--132. doi:10.36045/bbms/1080056165. https://projecteuclid.org/euclid.bbms/1080056165