Vol. 57, No. 1, 1975

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Compact convergence and the order bidual for C(X)

William Alan Feldman and James Franklin Porter

Vol. 57 (1975), No. 1, 113–124

An order-theoretic characterization of the topology of compact convergence on the lattice C(X) of all continuous real-valued functions on X is provided for a realcompact space X, analogous to the order unit characterization for compact X. The approach is to generalize the concept of an order unit to permit consideration of locally convex topologies. The characterization is then achieved by viewing C(X) as a subspace of its order bidual. In addition, the bidual is employed to provide an order-theoretic description of the continuous convergence structure on C(X).

Mathematical Subject Classification 2000
Primary: 46E05
Secondary: 54C40
Received: 10 October 1973
Revised: 12 April 1974
Published: 1 March 1975
William Alan Feldman
James Franklin Porter