Bornological projective limits of inductive limits of normed spaces

[EN] 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.The research of J. Bonet was partially supported by MEC and FEDER Project MTM2007-62643, GV Project Prometeo 2008/101 and the net MTM 2007-30904-E (Spain).Bonet Solves, JA.; Wegner, S. (2011). Bornological projective limits of inductive limits of normed spaces. Functiones et Approximatio, Commentarii mathematici. 44(2):227-242. doi:10.7169/facm/1308749126S22724244