Introduction. Let G be a locally compact, connected topological group (satisfying the second countability axiom). Let G* be a compact space which contains a dense subset G' homeomorphic to the space G and is such that G* — G' is totally disconnected. Then, Freudenthal has proved [l, Satz IX, p. 277]1 that the set G*-G' consists of at most two distinct points. Actually, Freudenthal's theorem eve...