Measure, Integration & Real Analysis · Problem 6D.6
L^p Spaces — Sheldon Axler
Mathematics — Measure Theory · norms-finite-dimensional
Problem
Suppose n∈Z+.
(a) Prove that all norms on Fn have the same convergent sequences, the same open sets, and the same closed sets.
(b) Prove that all norms on Fn make Fn into a Banach space.