Order-bounded convergence structures on spaces of continuous functions

Abstract

AbstractThis paper deals with solid topologies and convergence structures on the vector-lattice CX (the set of all continuous real-valued functions on a space X): the closed ideals and locally convex topologies associated with such structures are studied in particular. The work stems from E. Hewitt's paper on bounded linear functionals, touches on the classical theorems of L. Nachbin, T. Shirota and others (determining when the topology of compact convergence is barrelled or bornological), and extends some recent results on the duality between x and CX.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 35; secondary 54 A 20.