Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 481500 (2004) 

Ball versus distance convexity of metric spacesThomas FoertschInstitute for Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland, email: 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:
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