Partial actions of groups on profinite spaces

DOI10.4995/AGT.2024.18049arXiv2101.04779OpenAlexW3118641029MaRDI QIDQ6127783

Author name not available (Why is that?)

Publication date: 14 April 2024

Published in: (Search for Journal in Brave)

Abstract: We show that for a partial action

e t a

with closed domain of a compact group

G

on a profinite space

X

the space of orbits

X /! s i m_{G}

is profinite, this leads to the fact that when

G

is profinite the enveloping space

X_{G}

is also profinite. Moreover, we provide conditions for the induced quotient map

p i_{G} : X o X /! s i m_{G}

of

e t a

to have a continuous section. Relations between continuous sections of

p i_{G}

and continuous sections of the quotient map induced by the enveloping action of

e t a

are also considered. At the end of this work we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.

Full work available at URL: https://arxiv.org/abs/2101.04779

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Partial actions of groups on profinite spaces

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6127783)