Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 2, pp. 481-500 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 481-500 (2004) |
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Ball versus distance convexity of metric spacesThomas FoertschInstitute for Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland, e-mail: foertsch@math.unizh.chAbstract: 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 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
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