Bornological projective limits of inductive limits of normed spaces
  We establish a criterion to decide when a countable projective limit of countable inductive limits of normed spaces is bornological. We compare the conditions occurring within our criterion with well-known abstract conditions from the context of homological algebra and with conditions arising within the investigation of weighted PLB-spaces of continuous functions. 
Jos\'e Bonet and Sven-Ake Wegner
math.FA