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A note on Pt-ideals

Published online by Cambridge University Press:  09 April 2009

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
Copyright
Copyright © Australian Mathematical Society 1972

References

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