A Note On Separating Function Sets

Raushan Buzyakova; Oleg Okunev

A Note On Separating Function Sets

General Topology 2017-08-29 v1

Authors: Raushan Buzyakova , Oleg Okunev

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.

Keywords

general topology

Cite

@article{arxiv.1708.07927,
  title  = {A Note On Separating Function Sets},
  author = {Raushan Buzyakova and Oleg Okunev},
  journal= {arXiv preprint arXiv:1708.07927},
  year   = {2017}
}

Comments

Lobachevskii Journal of Mathematics, accepted, 2017

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