A Note on Minimal Separating Function Sets

2018/09/13 by Raushan Buzyakova, Buzyakova, Raushan, Oleg Okunev +1
Mathematics · #54A25 #54C35 #54E45 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54A25 #msc:54C35 #msc:54E45

paper · pdf · doi:10.48550/arxiv.1809.05186

arxiv created 2018/09/13 · arxiv updated 2018/09/17

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 X² 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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