Date of Award
5-1974
Degree Type
Thesis
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Supervisor
T. Husain
Abstract
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.
Recommended Citation
Rosa, Domenico, "On Locally m-convex Function Algebras" (1974). Open Access Dissertations and Theses. Paper 3720.
http://digitalcommons.mcmaster.ca/opendissertations/3720