A Banach-Steinhaus theorem for sets of continuous linear mappings on topological modules which are Baire spaces is proved, and some consequences of it are derived. Mathematics Subject Classification: 46H25, 46S10, 46E10

A sufficient condition for the insertion of a contra-continuous (resp. Baire-one) function between two comparable real-valued functions is given on the topological spaces that Λ-sets are open (resp. Gδ-sets).

This is the first of two lectures on measurable chromatic numbers given in June 2010 at the University of Barcelona. Our main result here is that acyclic locally finite analytic graphs on Polish spaces admit Baire measurable 3-colorings.

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...