## 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