1. The problem statement, all variables and given/known data 2. Relevant equations I think this is relevant: 3. The attempt at a solution A topological isomorphism implies that T and T-1 are bounded and given is that all cauchy sequences in E are convergent. But if that's the case then by boundedness all convergent sequences are bounded in het norm of F and are thus also Cauchy seqeunces. Am I thinking in the right direction?