A new proof for the bornologicity of the space of slowly increasing   functions
  A. Grothendieck proved at the end of his thesis that the space of slowly increasing functions and the space 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. 
Julian Larcher and Jochen Wengenroth
math.FA