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Compatible Tight Riesz Orders on the Group of Automorphisms of an 0-2-Homogeneous Set: Addendum

Published online by Cambridge University Press:  20 November 2018

Gary Davis  and
Colin D. Fox
Gary Davis
Affiliation:
La Trobe University, Melbourne, Australia
Colin D. Fox
Affiliation:
La Trobe University, Melbourne, Australia
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Abstract

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The purpose of this note is to show that Theorem 8 of Davis and Fox [1] is sharp. That is, we show that the following result is valid.

THEOREM. Let Ω be an 0-2-homogeneous ordered set. Then Tρ(respectively, Tƛ ) is a maximal compatible tight Riesz order if and only if Ω has a countable cofinal(respectively, coinitial) subset.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 664 - 665
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Davis, G. E. and Fox, C. D., Compatible tight Riesz orders on the automorphism group of an 0-2-homogeneous set, Can. J. Math. 28 (1976), 1076–1081.Google Scholar