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arXiv · 1708.07927

A Note On Separating Function Sets

Raushan Buzyakova·Oleg Okunev
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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.

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Raushan Buzyakova, Oleg Okunev. 2017-08-26. A Note On Separating Function Sets. https://arxiv.org/abs/1708.07927

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