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

✍ Scribed by Batildo Requejo

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 252 KB
• Volume: 77
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00143-5

✦ Synopsis

Let C(X) be the algebra of all K-valued continuous functions (K = ~. or C) on a normal (and TO topological space X, and let ~'x be the topology of compact convergence on C(X).

The following properties are well known:

(ill) the only closed ideals of (C(X), ~'x) ate the ideals of the form {.f E C(X): f(C) = O} (with C c_ X). In this paper we prove that properties (i), (ii) and (iii) characterize the topology 7x.