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Automorphic compactifications and the fixed point lattice of a totally-ordered set

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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When a totally-ordered set Ω has no points fixed by all automorphisms ve equip Ω with the support topology which has fixed-sets of automorphisms as basic closed sets. There is a mapping from Ω into the set of prime dual ideals of the lattice Φ(Ω) of basic closed sets and this allows us to classify the points of Ω as excellent, isolated, static, or extraordinary. There is an action of the group of automorphisms of Ω on the lattice Φ(Ω) and this allows us to see that automorphisms of Ω preserve the prime dual ideal classification of points of Ω. When the empty set is a basic closed subset of Ω the dual spectrum of Φ(Ω) is a compact T0 space (Hausdorff when all points of Ω are excellent) containing Ω as a dense subspace and allowing an extension of each automorphism of Ω ťo a homeomorphism of the dual spectrum.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 101 - 109
Copyright
Copyright © Australian Mathematical Society 1975

References

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