On B() and Br() locally convex spaces

Abstract

1. Introduction. In his papers (2), (3) and (4), and in his book (5), Husain studied the locally convex, Hausdorff, linear topological spaces (hereafter abbreviated to l.c. spaces) which he called B() spaces and Br() spaces and which satisfy weakened forms of the B completeness and Br completeness conditions of Ptak (8). L.c. spaces satisfying another weakening of the Br completeness condition were studied by Persson in (7) and were called by him, weakly t-polar. We consider some examples in connexion with these spaces.