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Strict convexity of sets in analytic terms

Part of: General convexity

Published online by Cambridge University Press:  09 April 2009

Leoni Dalla  and
Telemachos Hatziafratis
Leoni Dalla
Affiliation:
The University of Athens, Department of Mathematics, Panepistemiopolis 15784, Athens, Greece, e-mail: [email protected], [email protected]. gr
Telemachos Hatziafratis
Affiliation:
The University of Athens, Department of Mathematics, Panepistemiopolis 15784, Athens, Greece, e-mail: [email protected], [email protected]. gr
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Abstract

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We compare the geometric concept of strict convexity of open subsets of Rn with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2N-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.

Keywords

strictly convex set2N-strictly convex setdefining functionexhaustion of a convex set.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 49 - 62
Copyright
Copyright © Australian Mathematical Society 2006

References

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