On a valuation field invented by A. Robinson and certain structures connected with it

We clarify the structure of the non-archimedean valuation field ^ρ R which was introduced by A. Robinson, and of theρ-non-archimedean hulls of Banach algebras and Lie groups. (For Banach spaces this construction is due to W. A. J. Luxemburg.) In particular, we show that any two infinite-dimensional real normed spaces have a pair of isometrically isomorphicρ-non-archimedean hulls. Dedicated to the memory of A. Robinson on the occasion of the 70th anniversary of his birth.