In the predecessor [16] of this paper the canonical subgroup (Fat Delta) ∆(G) of a compact abelian group G was studied. It is the sum of all closed disconnected subgroups of G and it appeared before in the literature (see [28]) as td(G), defined for arbitrary topological groups and motivated by completely different considerations. We introduce and compare further functorial subgroups of general topological groups and study their relationships with ∆(G) and td(G).
