Una nota sobre espacios localmente completos

Abstract

Using standard locally convex spaces techniques, it is shown that local completeness is preserved under the formation of closed subspaces, projective limits, Cartesian products and locally convex direct sums. We also prove that if every bounded set in a locally convex space is contained in a bounded disk that generates a reflexive space, then the space is semi-reflexive and that a regular inductive limit of such locally reflexive spaces is also semi-reflexive.