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Ball versus distance convexity of metric spaces


Foertsch, T (2004). Ball versus distance convexity of metric spaces. Beiträge zur Algebra und Geometrie, 45(2):481-500.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Heldermann
ISSN:0138-4821
Additional Information:© 2004 Heldermann Verlag
Official URL:http://www.emis.de/journals/BAG/vol.45/no.2/11.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2093020

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