+ +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. + + +