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The order-bound topology on Riesz spaces

Published online by Cambridge University Press:  24 October 2008

Yau-Chuen Wong
Yau-Chuen Wong
Affiliation:
United College, The Chinese University of Hong Kong, Hong Kong
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Extract

1. Introduction. Let (X, C) be a Riesz space (or vector lattice) with positive cone C. A subset B of X is said to be solid if it follows from |x| ≤ |b| with b in B that x is in B (where |x| denotes the supremum of x and − x). The solid hull of B (absolute envelope of B in the terminology of Roberts (2)) is denoted to be the smallest solid set containing B, and is denoted by SB. A locally convex Hausdorff topology on (X, C) is called a locally solid topology if admits a neighbourhood-base of 0 consisting of solid and convex sets in X; and (X, C, ), where is a locally solid topology, is called a locally convex Riesz space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 587 - 593
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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