Reduction of the problem of character continuity in m-pseudoconvex algebras

In this paper, we extend the PG, Dixon and J. Esterle's approach of E.A. Michael problem to the class of complex. complete, metrizable m-pseudoconvex algebras. We show that if discontinuous characters do exist on some complete. metrizable m-pseudoconvex algebras, then every projective limit lim(C-Pn, F-n)(n is an element ofN*) not equal theta. where F-n : C-Pn --> C-Pn is entire, p(n) is an element of N*. We construct. also, a complete, metrizable m-pseudoconvex algebras epsilon such that if there exist discontinuous characters oil some complete metrizable m-pseudoconvex algebra there must exist some on epsilon.