Concerning continuity of inverse in quotients of topological algebras

Abstract

We construct a commutative complete unital locally convex algebra A, so that the operation of taking an inverse in A, x→x^-1,  is continuous on the group G(A) of all invertible elements in A, but there is a closed ideal I ⊂ A such that the operation of taking an inverse is discontinuous in thequotient algebra A/I.