On points avoiding measures

2023/11/09 by Borodulin-Nadzieja, Piotr, Ranchynski, Artsiom · 1 citation
#FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2311.05751

Abstract

We say that an element x of a topological space X avoids measures if for every Borel measure μ on X if μ(\x\)=0, then there is an open U\ni x such that μ(U)=0. The negation of this property can viewed as a local version of the property of supporting a strictly positive measure. We study points avoiding measures in the general setting as well as in the context of ω^∗, the remainder of Stone-Čech compactification of ω.

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