Dear gap forum,
I have two questions as following:
Let G be a compact group
(i) Let f(x)= \mu(C_G(x)) where \mu is Haar measure. Is f a continuous
function?
(ii) Let f(x)= \chi_a(x,y) where y \in G and a={(x,y) \in G^2 | xy=yx }. Is f
a continuous function?
I will be more grateful for any known results or references.
Best regards,
R. Rezaei
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