Bidualização de espaços afins

Abstract

Main concepts on a ne space are presented. Let X be an a ne space modelled on a vector space V and X? = A(X, R) be the a ne dual of X, that is, the vector space of all a ne maps from X to the real line. It is well known that in the case of a nite dimensional vector space V , the bidual V ∗∗ is isomorphic to V . We consider the vectorial bidual (X? ) ∗ of X and an immersion of the a ne space X into its vectorial bidual. We present a discussion how to de ne the a ne bidual X?? of X.