The Hahn-Banach Theorem: a proof of the equivalence between the analitic and geometric versions

Abstract

We present here a simple and direct proof of the classic geometric version of Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal implication, and the direct proofs of both versions, are already well kown, but they are also summarized. For the complex case, in both versions the Hahn-Banach Theorem is deduced from the real case, as it is well known.