### The Hahn-Banach Theorem for Real Vector Spaces (Isabelle/Isar)

Author: Gertrud Bauer, Technische Universität München

This directory contains the proof of the Hahn-Banach theorem for real vectorspaces, following H. Heuser, Funktionalanalysis, p. 228 -232. The Hahn-Banach theorem is one of the fundamental theorems of functioal analysis. It is a conclusion of Zorn's lemma.

Two different formaulations of the theorem are presented, one for general real vectorspaces and its application to normed vectorspaces.

The theorem says, that every continous linearform, defined on arbitrary subspaces (not only one-dimensional subspaces), can be extended to a continous linearform on the whole vectorspace.