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Continuity of representations of topological groups

Comparatively recently a new class of topological groups (TG) has been studied called exotic groups (EG), which have no continuous non-trivial unitary representations; see [1], [2] and [3]. In this paper we investigate the properties of EGs with respect to the operations of inductive and projective limits. A theorem will be proved on the construction of EGs for non-metrizable spaces. It is shown that the EGs form a full subcategory of the category of TGs.