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Compatible tight Riesz orders on C(X)

Published online by Cambridge University Press:  09 April 2009

Elizabeth Loci
Affiliation:
Department of Mathematics, La Trobe University, Victoria 3083, Australia.
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Abstract

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The pointwise order makes the group C(X) of continuous real-valued functions on a topological space X a lattice-ordered group. We give a characterization of the compatible tight Riesz orders on C(X), and also of their maximal tangents, in terms of the zero-sets of X. The space of maximal tangents of a given compatible tight Riesz order T is studied, and consequently the concept of the T-radical of C(X) is introduced, the T-radical being the intersection of all the maximal tangents of T.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

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