Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T15:46:20.105Z Has data issue: false hasContentIssue false
  • English
  • Français

Compatible tight Riesz orders on C(X)

Published online by Cambridge University Press:  09 April 2009

Elizabeth Loci
Elizabeth Loci
Affiliation:
Department of Mathematics, La Trobe University, Victoria 3083, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 371 - 379
Copyright
Copyright © Australian Mathematical Society 1976

References

Fuchs, L. (1963), Partially Ordered Algebraic Systems (Pergamon Press, Oxford, 1963).Google Scholar
Gillman, L. and Jerison, M. (1960), Rings of Continuous Functions (Van Nostrand, Princeton, 1960).CrossRefGoogle Scholar
Holland, C. (1963), ‘The lattice-ordered group of automorphisms of an ordered set’, Mich. Math J. 10, 399–408.CrossRefGoogle Scholar
Maclane, Saunders (1971), Categories for the Working Mathematician (Springer-Verlag, New York, 1971).Google Scholar
Miller, J. B. (1973), ‘Quotient groups and realization of tight Riesz groups’, J. Austral. Math. Soc. 16, 416–430.CrossRefGoogle Scholar
Wirth, A. (1973), ‘Compatible tight Riesz orders’, J. Austral. Math Soc. 15, 105–111.CrossRefGoogle Scholar