Bulletin of the Belgian Mathematical Society - Simon Stevin

A characterization of trans-separable spaces

J.C. Ferrando, Jerzy Kąkol, and M. López Pellicer

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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

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

First available in Project Euclid: 28 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54E15: Uniform structures and generalizations 54C35: Function spaces [See also 46Exx, 58D15] 46A50: Compactness in topological linear spaces; angelic spaces, etc.

Trans-separable space web-compact space angelic space


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.https://projecteuclid.org/euclid.bbms/1190994210

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