Polish globalization of Polish group partial actions

2016/02/20 by Pinedo, Hector, Uzcategui, Carlos
#54E35 #54E50 #FOS: Mathematics #Logic (math.LO) #Primary 54H15 #Secondary 54H05

paper · doi:10.48550/arxiv.1602.06433

Abstract

Let X be a separable metrizable space. We establish a criteria for the existence of a metrizable globalization for a given continuous partial action of a separable metrizable group G on X. If G and X are Polish spaces, we show that the globalization is also a Polish space. We also show the existence of an universal globalization for partial actions of Polish groups.

Related

• Borel Globalizations of Partial Actions of Polish Groups
• Global and local boundedness of Polish groups
• A universal Polish G-space
• The open mapping principle for partial actions of polish groups
• Partial actions on quotient spaces and globalization