A Note On Separating Function Sets

Raushan Buzyakova; Oleg Okunev

paper

A Note On Separating Function Sets

arXiv:1708.07927

Abstract

We study separating function sets. We find some necessary and sufficient conditions for $C_{p} (X)$ or $C_{p}^{2} (X)$ to have a point-separating subspace that is a metric space with certain nice properties. One of the corollaries to our discussion is that for a zero-dimensional $X$ , $C_{p} (X)$ has a discrete point-separating space if and only if $C_{p}^{2} (X)$ does.

Lobachevskii Journal of Mathematics, accepted, 2017