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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

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