Order convergence on Archimedean vector lattices and applications

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University of Pretoria

Abstract

We study the order convergence of sequences on a vector lattice. It is shown that this mode of convergence is induced by a convergence structure. One such a convergence structure is defined and its properties are studied. We apply the results obtained to find the completion of C(X). We also obtain a Banach-Steinhauss theorem for ó-order continuous operators.

Description

Dissertation (Magister Scientiae)--University of Pretoria, 2007.

Keywords

Vector lattice, Convergence structure, Order convergence, UCTD

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Citation

Van der Walt, J 2005, Order convergence on Archimedean vector lattices and applications, Magister dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/26901 >