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Locally compact tight Riesz groups

Published online by Cambridge University Press:  09 April 2009

Andrew Wirth
Andrew Wirth
Affiliation:
Department of Mathematics, Monash UniversityClayton Victoria 3168, Australia
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It is known that a strongly archimedean locally compact tight Riesz group without pseudozeros is essential Rm with the usual topology and tight order. We show that a locally compact tight Riesz group, (G, ≦), without pseudozeros, is algebraically and topologically isomorphic with Rm ⊕ D, where D is discrete. Rm ⊕ {0} is a clopen oideal; and we give necessary and sufficient conditions for G to be isomorphic with Rm ⊕ D in all respects. Further (G, ≦) contains an oideal isomorphic with Rm ⊕ ∑ℵZ and G is isomorphic with it if and only if (G, ≦, U) is interval-compact.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 2 , March 1975 , pp. 247 - 251
Copyright
Copyright © Australian Mathematical Society 1975

References

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