Order convergence on Archimedean vector lattices and applications

Description

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. / Dissertation (Magister Scientiae)--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

Links & Downloads

1. http://hdl.handle.net/2263/26901
2. 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 >
3. http://upetd.up.ac.za/thesis/available/etd-02062006-130754/

Tags

Vector lattice

Convergence structure

Order convergence

UCTD

Additional Fields

Identifer	oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/26901
Date	06 February 2006
Creators	Van der Walt, Jan Harm
Contributors	Anguelov, Roumen, [e-mail]
Source Sets	South African National ETD Portal
Detected Language	English
Type	Dissertation
Rights	© 2005, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.