Compactly supported locally constant function
= Compactly supported locally constant function
{title2=$C_c^\infty(X)$}
The space $C_c^\infty(X)$ consists of locally constant complex functions with compact support. On a <locally profinite group>, finite compact-open coset covers of the support show that every such function is fixed by one common <compact-open subgroup> under right translation. The symbol infinity describes local constancy in this context, not real differentiability.