An example of a non non-archimedean Polish group with ample generics

Malicki, Maciej

doi:10.1090/proc/13017

An example of a non non-archimedean Polish group with ample generics
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by Maciej Malicki PDF

Proc. Amer. Math. Soc. 144 (2016), 3579-3581 Request permission

Abstract:

For an analytic $P$-ideal $I$ we denote by $S_I$ the Polish group of all the permutations of $\mathbb{N}$ with support in $I$, equipped with a topology given by the corresponding submeasure on $I$. We show that if $\mbox {Fin} \subsetneq I$, then $S_I$ has ample generics. This implies that there exists a non non-archimedean Polish group with ample generics.

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