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

Let 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). llowing properties are well known: 1. (X), τX) is a locally m-convex K-algebra; he set C(X): 0 ∉ (K) is open in (C(X), τX) for each compact subset K of X; 0806 118 the only closed ideals of (C(X), τX) are the ideals of the form C(X): (C) = 0 0806 118 (with C ⊆ X). s paper we prove that properties (i), (ii) and (iii) characterize the topology τX.