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Quasi-concave functions and convex convergence to infinity

Published online by Cambridge University Press:  17 April 2009

Gerald Beer
Gerald Beer
Affiliation:
Department of MathematicsCalifornia State UniversityLos Angeles CA 90032United States of America
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Abstract

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By a convex mode of convergence to infinity 〈Ck〉, we mean a sequence of nonempty closed convex subsets of a normed linear space X such that for each k, Ck+1 ⊆ int Ck and and a sequence 〈xn〉 is X is declared convergent to infinity with respect to 〈Ck〉 provided each Ck contains xn eventually. Positive convergence to infinity with respect to a pointed cone with nonempty interior as well as convergence to infinity in a fixed direction fit within this framework. In this paper we study the representation of convex modes of convergence to infinity by quasi-concave functions and associated remetrizations of the space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 81 - 94
Copyright
Copyright © Australian Mathematical Society 1999

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