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Compatible tight Riesz orders on groups of integer-valued functions

Published online by Cambridge University Press:  17 April 2009

Gary Davis
Gary Davis
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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Abstract

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A construction due to Reilly is extended to show that there is a correspondence between compatible tight Riesz orders on ZX and non-principal filters on X. The maximal compatible tight Riesz orders are in one-to-one correspondence with non-principal ultra-filters, and are dual prime subsets of the positive set of ZX. Conversely every dual prime algebraic Riesz order is maximal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 383 - 390
Copyright
Copyright © Australian Mathematical Society 1975

References

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