Concerning continuity of inverse in quotients of topological algebras
Keywords:
topological algebra, locally convex algebra, quotient algebra, continuity of an inverse
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.
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