Continuity conditions for finite-dimensional representations of some locally bounded groups
The author proves necessary and sufficient conditions for the continuity of finite-dimensional representations of some topological groups. The conditions are formulated in terms of the variation of the representation at the identity of the group. The conditions are found for the following groups: -- locally oddly divisible groups; -- topological groups in which the open normal subgroups form a neighborhood base of the identity; -- almost divisible, non-discrete, locally pseudo-compact groups; -- (almost) connected locally compact groups. An application of the above result to the approximation of continuous quasirepresentations of almost connected locally compact groups is given.
scientific article; zbMATH DE number 5136642
scientific article