A characterization of the topology of compact convergence on C(X)

AbstractLet C(X) be the algebra of all K-valued continuous functions K = R or C on a normal (and T1) topological space X, and let τX be the topology of compact convergence on C(X).The following properties are well known: 1.(i) (C(X), τX) is a locally m-convex K-algebra;2.(ii) the set C(X): 0 ∉ (K) is open in (C(X), τX) for each compact subset K of X; 0806 1183.(iii) the only closed ideals of (C(X), τX) are the ideals of the form C(X): (C) = 0 0806 118 (with C ⊆ X).In this paper we prove that properties (i), (ii) and (iii) characterize the topology τX