Continuity and hypocontinuity for bilinear maps (Q797089)

Let E, F and G be metric linear spaces and \(b:E\times F\to G\) a separately continuous bilinear map. By employing the notion of K- convergent sequence and K-bounded sets, we give a general hypocontinuity result which holds without completeness assumptions on any of the spaces and which contains the Bourbaki hypocontinuity result for Frechet spaces as a special case. The classical Mazur-Orlicz result on joint continuity is also obtained.