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Continuity properties of vector-valued convex functions

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

L. I. Trudzik
L. I. Trudzik
Affiliation:
Department of MathematicsUniversity of MelbourneParkville, Victoria 3052, Australia
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Abstract

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We extend various characterizations of scalar-valued lower semicontinuity and determine their relationship to the continuity of vector-valued convex functions. Order completeness of the range space is not assumed.

Keywords

vector-valued convex functionscontinuouslower semicontinuouslower quasicontinuous.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices 46A55: Convex sets in topological linear spaces; Choquet theory 90C48: Programming in abstract spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 404 - 415
Copyright
Copyright © Australian Mathematical Society 1984

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