An analytic structure emerging in presence of infinitely many odd coordinates

Abstract

This is a contribution to the program of featuring even geometry as a ``collective effect in infinite-dimensional odd geometry,'' as suggested by Manin. We show that the (Gel'fand) spectrum of the locally convex nonstandard hull (in the sense of Luxemburg) of a grassmannian algebra with infinitely many odd generators contains a nontrivial analytic part.