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permutations – Haar touchstone on $S_omega$
Let $S_omega$ breathe the gathering of bijections $f:omegato omega$. Endow $omega$ with the discrete topology and let $S_omega$ breathe endowed with the subspace topology of $omega^omega$, the place $omega^omega$ carries the product topology. So, $(S_omega, circ)$ is a regionally compact group and so there’s a Haar touchstone on $S_omega$.
Is there a constructive description of the Haar touchstone on $S_omega$?
If sure: Let $M$ breathe the clique of “finitely bounded permutations of $omega$, that is, $$M= < K)).$$ What is the Haar touchstone of $M$, and of $S_omega setminus M$?
(A rectify and comprehensible retort to both query will breathe accepted.)
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