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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

7 votes
1 answer
840 views

Hahn-Banach theorem for arbitrary locally compact fields?

Does anyone know if the Hahn-Banach theorem is true for every locally compact field? Specifically, let $F$ be a finite algebraic extension of either $Q_p$, the $p$-adic completion of $Q$, or of $S_p$ …