[GAP Forum] question

[rashid rezaei]

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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