On Locally m-convex Function Algebras

Abstract

<p>In this thesis an analogue of B-completeness is defined for locally m-convex algebras. Namely, a commutative locally m-convex algebra A is said to be a B(£) algebra if every continuous and almost open homomorphism from A onto any locally m-Convex algebra is open. A characterization is obtained of those completely regular spaces X for which C(X) with the compact-open topology is a B(£) algebra. Permanence properties of B(£) algebras are investigated, and extensions of the closed graph theorem are obtained. In addition, a categorical treatment of commutative locally m-convex algebras and their relationship with completely regular spaces is given.</p>