I have recently come across a statement in the book: Kazhdan's property (T) by B. Bekka, P. de la Harpe, A. Valette at the beginning Appendix F.2. Fell topology on sets of unitary representations.
Let $G$ be a topological group. One would like to define a topology on the family of equivalences classes of unitary representations of $G$. There is a problem since this family is not a set.
Can anyone elaborate on this, why is this family not a set (when $G$ is not locally compact abelian or compact)?