Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 481-500 (2004)
Ball versus distance convexity of metric spaces
Thomas FoertschInstitute for Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland, e-mail: firstname.lastname@example.org
Abstract: We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when considering the Euclidean product.
Classification (MSC2000): 53C70; 51F99
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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.