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Order-bounded convergence structures on spaces of continuous functions

Published online by Cambridge University Press:  09 April 2009

M. Schroder
M. Schroder
Affiliation:
Department of Mathematics University of Waikato, New Zealand
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Abstract

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This 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 39 - 61
Copyright
Copyright © Australian Mathematical Society 1979

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