A new proof for the bornologicity of the space of slowly increasing functions

Abstract

A. Grothendieck proved at the end of his thesis that the space $\mathcal{O}_M$ of slowly increasing functions and the space $\mathcal{O}_{C}'$ of rapidly decreasing distributions are bornological. Grothendieck's proof relies on the isomorphy of these spaces to a sequence space and we present the first proof that does not utilize this fact by using homological methods and, in particular, the derived projective limit functor.