Resumen de Limits and the Ext functor

Jesús María Fernández Castillo , Marilda A. Simoes

• We show the identity Ext(limà X®;R) = lim! Ext(X®;R) for projective limits of quasi-Banach spaces X®. The proof is derived from a pull-back lemma asserting that a topologically exact sequence 0 ! R ! E ! Z ! 0 of locally pseudoconvex spaces is the pull-back of an exact sequence of quasi-Banach spaces. Among the consequences we show that exact sequences 0 ! R ! E ! Z ! 0 of locally pseudoconvex spaces come induced by quasi-linear maps, which extends a result of Kalton for Fr¶echet spaces; and that projective limits of K-spaces are K-spaces.