Structure of locally compact groups with metrizable connected components up to negligible subsets (Q1099260)

It is shown that, after removal of a suitable negligible subset N, a locally compact group G with non-trivial metrizable connected components is of simple topological structure, namely, a product of a discrete space, the space of irrationals, and a Cantor spaces. N can be chosen so as to respect the algebraic and topological structure of G and its Haar measure. Consequently, such a group G has a large supply of \(G_{\delta}\)-subsets of Cantor type. Some of the results have analogues in coset spaces G/H.