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Inextensible Riesz spaces

Published online by Cambridge University Press:  24 October 2008

D. H. Fremlin
D. H. Fremlin
Affiliation:
University of Essex, Colchester
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Extract

My aim in this paper is to give an abstract characterization of the C∞ spaces described in (6) or (9), and to develop some of the remarkable special properties of these spaces. Although the subject is in some ways highly specialized, inextensible and sequentially inextensible spaces seem common enough (they include all spaces of the forms Rx and L0) to be worth studying, and I have already employed them in the proof of more general results (1).

In the first section I set out those properties that can be described in simple Riesz space terms; much of this work has already been published in slightly different forms. In the second part I go on to questions that arise when we impose a topology on an inextensible Riesz space. Finally, in the third section, I discuss some problems, arising from the work before, which are related to the famous measurable cardinal problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 1 , January 1975 , pp. 71 - 89
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Fremlin, D. H.On the completion of locally solid vector lattices. Pacific J. Math. 43 (1972), 341–347.Google Scholar
(2)Fremlin, D. H.Topological Riesz spaces and measure theory (Cambridge University Press, 1973).Google Scholar
(3)Keisler, H. K. & Tarski, A.From accessible to inaccessible cardinals, etc. Fund Math. 53 (1963–1964), 225–308.Google Scholar
(4)Luxemburg, W. A. J.Is every integral normal? Bull. American Math. Soc. 73 (1967), 685–688.Google Scholar
(5)Luxemburg, W. A. J. & Zaanen, A. C.Notes on Banach function spaces VII. Nederl. Akad. Wetensch. Proc. Ser. A 66 (1963), 669–681.Google Scholar
(6)Luxemburg, W. A. J. & Zaanen, A. C.Riesz spaces I (North-Holland, 1971).Google Scholar
(7)Peressnvi, A. L.Ordered topological vector spaces (Harper & Row, 1967).Google Scholar
(8)Solovay, R. M.Real-valued measurable cardinals. Proc. Symposia in Pure Mathematics 13 (Axiomatic Set Theory), Part 1 (American Math. Soc. 1971), pp. 397–428.Google Scholar
(9)Vulikh, B. Z. Introduction to the theory of partially ordered Spaces (Wolters-Noordhoff, 1967).Google Scholar
(10)Prikry, K.On σ-complete prime ideals in Boolean algebras. Colloq. Math. 22 (1971), 209–214.CrossRefGoogle Scholar