Closed ideals in topological algebras: A characterization of the topological Φ-algebra C_k(x)

摘要

Let A be a uniformly closed and locally m-convex Φ-algebra. We obtain internal conditions on A stated in terms of its closed ideals for A to be isomorphic and homeomorphic to C_k (X), the Φ-algebra of all the real continuous functions on a normal topological space X endowed with the compact convergence topology.