Universally measurable subgroups of countable index

Details Universally measurable subgroups of countable index Universally measurable subgroups of countable index

2011-04-17

arxiv.org/abs/1104.3343v1

J. Symbolic Logic 75 (2010), no. 3, 1081-1086

Mathematics

Logic

Scientific paper

It is proved that any countable index, universally measurable subgroup of a
Polish group is open. By consequence, any universally measurable homomorphism
from a Polish group into the infinite symmetric group $S_\infty$ is continuous.
It is also shown that a universally measurable homomorphism from a Polish group
into a second countable, locally compact group is necessarily continuous.

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