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A note on Pt-ideals

Published online by Cambridge University Press:  09 April 2009

G. T. Spirason  and
E. Strzelecki
G. T. Spirason
Affiliation:
Monash University, Victoria, 3168, Australia.
E. Strzelecki
Affiliation:
Monash University, Victoria, 3168, Australia.
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Let E be a vector lattice in the sense of [2]. Two elements a, b in E are said to be disjoint (written a⊥b) if ′a′^′b′ = 0. For any subset A of E, A⊥ is the set If A is a one point set {a}, then we shall use a⊥ for {a}⊥. A⊥⊥ is denned by A⊥⊥ = {A⊥}⊥. A subset B of E is said to be a polar if it is of the form A⊥ for some subset A of E. It is well known [1] that the set of all polars of E ordered by inclusion forms a Boolean algebra. We shall denote this algebra by B, and M will mean the set of all maximal ideals of B. The following properties of polars will be used in the paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 304 - 310
Copyright
Copyright © Australian Mathematical Society 1972

References

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