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Convergence in partially ordered groups

Published online by Cambridge University Press:  20 January 2009

Andrew Wirth
Andrew Wirth
Affiliation:
Monash University, Clayton, Victoria
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Abstract

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Relative uniform limits need not be unique in a non-archimedean partially ordered group, and order convergence need not imply metric convergence in a Banach lattice. We define a new type of convergence on partially ordered groups (R-convergence), which implies both the previous ones, and does not have these defects. Further R-convergence is equivalent to relative uniform convergence on divisible directed integrally closed partially ordered groups, and to order convergence on fully ordered groups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 3 , June 1973 , pp. 239 - 246
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

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