Functional Analysis - Normed Linear Space

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

Linear functional on a topological vector space

Suppose that T is a topologocal vector space. Prove that a linear functional f on T is continuous if and only if ker(f) is closed

Normed Linear Space

Suppose that N is a normed linear space. Prove that every linear functional on N is continuous if and only if N is finite dimensional.

Two-part question on a finite dimensional normed linear space

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Banach Space

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