Bulletin of the Belgian Mathematical Society - Simon Stevin

A characterization of trans-separable spaces

Abstract

The paper shows that a uniform space $X$ is trans-separable if and only if every pointwise bounded uniformly equicontinuous subset of the space of continuous real-valued functions $C_{c}(X)$ equipped with the compact-open topology is metrizable. This extends earlier results of Pfister and Robertson and also applies to show that if $C_{c}(X)$ is angelic then $X$ is trans-separable. The precise relation among DCCC spaces and trans-separable spaces has been also determined.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 493-498.

Dates
First available in Project Euclid: 28 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1190994210

Digital Object Identifier
doi:10.36045/bbms/1190994210

Mathematical Reviews number (MathSciNet)
MR2387046

Zentralblatt MATH identifier
1133.54014

Citation

Ferrando, J.C.; Kąkol, Jerzy; López Pellicer, M. A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 493--498. doi:10.36045/bbms/1190994210. https://projecteuclid.org/euclid.bbms/1190994210