Borel Globalizations of Partial Actions of Polish Groups

Carlos Uzcategui; Hector Pinedo

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arXiv · 1702.02611

Borel Globalizations of Partial Actions of Polish Groups

Carlos Uzcategui·Hector Pinedo

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Abstract

We show that the enveloping space $X_G$ of a partial action of a Polish group $G$ on a Polish space $X$ is a standard Borel space, that is to say, there is a topology $\tau$ on $X_G$ such that $(X_G, \tau)$ is Polish and the quotient Borel structure on $X_G$ is equal to $Borel(X_G,\tau)$. To prove this result we show a generalization of a theorem of Burgess about Borel selectors for the orbit equivalence relation induced by a group action and also show that some properties of the Vaught's transform are valid for partial actions of groups.

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BibTeX RIS

Carlos Uzcategui, Hector Pinedo. 2017-02-08. Borel Globalizations of Partial Actions of Polish Groups. https://arxiv.org/abs/1702.02611

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