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arXiv · 1809.05186

A Note on Minimal Separating Function Sets

Raushan Buzyakova·Oleg Okunev
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Abstract

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space $X$ having a minimal separating function set in $C_p(X)$ is equivalent to having a minimal separating collection of functionally open sets in $X$. We also identify a nice visual property of $X^2$ that may be responsible for the existence of a minimal separating function family for $X$ in $C_p(X)$. We then discuss various questions and directions around the topic.

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Raushan Buzyakova, Oleg Okunev. 2018-09-13. A Note on Minimal Separating Function Sets. https://arxiv.org/abs/1809.05186

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