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A characterization of pre-near-standardness in locally convex linear topological spaces

Published online by Cambridge University Press:  17 April 2009

J.J.M. Chadwick  and
R.W. Cross
J.J.M. Chadwick
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
R.W. Cross
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Let X be a locally convex linear topological space. A point z in an ultralimit enlargement of X is pre-near-standard if and only it is finite and for every equicontinuous subset S′ of the dual space X′, a point z′ belongs to *S′ ∩ μσ(X′, X) (0) only if z′ (z) is infinitesimal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 107 - 115
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Köthe, Gottfried, Topological vector spaces I (Translated by Garling, D.J.H.. Die Grundlehren der mathematischen Wissenschaften, Band 159. Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[2]Luxemburg, W.A.J., “A general theory of monads”, Applications of model theory to algebra, analysis, and probability (Internat. Sympos., Pasadena, California, 1967, 18–86). (Holt, Rinehart and Winston, New York, Chicago, San Francisco, Atlanta, Dallas, Montreal, Toronto, London, Sydney, 1969).Google Scholar
[3]Machover, Moshé, Hirschfeld, Joram, Lectures on non-standard analysis (Lecture Notes in Mathematics, 94. Springer-Verlag, Berlin, Heidelberg, New York, 1969).CrossRefGoogle Scholar
[4]Robinson, Abraham, Non-standard analysis (Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, 1966).Google Scholar