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Stability of wedges and semi-algebras

Published online by Cambridge University Press:  24 October 2008

Gavin Brown
Gavin Brown
Affiliation:
University of Liverpool
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Abstract

We obtain a simple new proof of Bonsall's characterization theorem for type 1 semi-algebras of continuous functions. An extension of our methods produces several new results on stability properties of wedges.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 365 - 376
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Barbeau, E. J. Commutative Semi-algebras. Ph.D. Thesis, University of Newcastle upon Tyne (1964).Google Scholar
(2)Bonsall, F. F.Semi-algebras of continuous functions. Proc. London Math. Soc. 10 (1960), 1–16.Google Scholar
(3)Bonsall, F. F.Semi-algebras of continuous functions. Proc. Int. Symposium on Linear Spaces(Jersualem, 1960), 101–114.Google Scholar
(4)Bonsall, F. F.On type 2 semi-algebras of continuous functions. Proc. London Math. Soc. 12 (1962), 133–143.CrossRefGoogle Scholar
(5)Bonsall, F. F.Algebraic properties of some convex cones of functions. Quart. J. Math. 14 (1963), 225–230.CrossRefGoogle Scholar
(6)Brown, G.Relatively type ο semi-algebras. Quart. J. Math. 18 (1967), 289–291.CrossRefGoogle Scholar
(7)Choquet, G. and Deny, J.Ensembles semi-reticulés et ensembles reticulés de fonctions continues. J. Math. Pures Appl. 36 (1957), 179–189.Google Scholar
(8)Guber, S.Masstheoretische Kennzeichnung gewisser Funktionenkegel. Arch. Math. 15 (1964), 58–70.CrossRefGoogle Scholar
(9)Guber, S.Darstellungs- und Stabilitätssätze für Funktionenkegel. Math. Zeit. 86 (1964), 63–74.CrossRefGoogle Scholar
(10)Kakutani, S.Concrete representation of abstract (M)-spaces. (A characterisation of the space of continuous functions). Ann. of Math. 42 (1941), 994–1024.CrossRefGoogle Scholar
(11)Pryce, J. D.On type F semi-algebras of continuous functions. Quart. J. Math. 16 (1965), 63–71.CrossRefGoogle Scholar
(12)Pryce, J. D. Cones and semi-algebras of continuous functions. Ph.D. Thesis. Univ. of Newcastle upon Tyne (1965).CrossRefGoogle Scholar
(13)Riesz, F. and SZ.-Nagy, B.Functional analysis (Ungar, 1955).Google Scholar