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Hyperconvex spaces revisited

Published online by Cambridge University Press:  17 April 2009

Marcin Borkowski ,
Dariusz Bugajewski  and
Hubert Przybycień
Marcin Borkowski
Affiliation:
Optimisation and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland, e-mail: mbork@venus.wmid.amu.edu.pl, ddbb@main.amu.edu.pl, hubert@main.amu.edu.pl
Dariusz Bugajewski
Affiliation:
Optimisation and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland, e-mail: mbork@venus.wmid.amu.edu.pl, ddbb@main.amu.edu.pl, hubert@main.amu.edu.pl
Hubert Przybycień
Affiliation:
Optimisation and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland, e-mail: mbork@venus.wmid.amu.edu.pl, ddbb@main.amu.edu.pl, hubert@main.amu.edu.pl
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Abstract

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In this paper we describe a construction of a large class of hyperconvex metric spaces. In particular, this construction contains well-known examples of hyperconvex spaces such as ℝ2 with the “river” metric or with the radial one.

Further, we investigate linear hyperconvex spaces with extremal points of their unit balls. We prove that only in the case of a plane (and obviously a line) is there a strict connection between the number of extremal points of the unit ball and the hyperconvexity of the space.

Some additional properties concerning the notion of hyperconvexity are also investigated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 191 - 203
Copyright
Copyright © Australian Mathematical Society 2003

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