# permutations – Haar touchstone on \$S_omega\$ retort

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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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