A note about congruences on subsemigroups of groups (Q1402900)

An elementary argument shows that a totally disconnected normal subgroup of a connected topological group is central. In the article [Arch. Math. 9, 33-38 (1958; Zbl 0095.02103)] \textit{K. H. Hofmann} has shown that by a skillful application of this argument a much wider class of interesting central results can be obtained. In the present paper, the authors offer a modification of the argument also applying it to congruences on subsemigroups of topological groups.