Measure, Integration & Real Analysis · Problem 6C.1

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · norm-continuous

Problem

Show that the map f↦∥f∥f \mapsto \|f\| from a normed vector space VV to F\mathbf{F} is continuous (where the norm on F\mathbf{F} is the usual absolute value).

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