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Minkowski versus Euclidean rank for products of metric spaces


Foertsch, T; Schroeder, V (2002). Minkowski versus Euclidean rank for products of metric spaces. Advances in Geometry, 2(2):123-131.

Abstract

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.

Abstract

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.

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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
Uncontrolled Keywords:Euclidean rank of metric spaces; Minkowski rank of metric spaces
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:06 Dec 2017 20:50
Publisher:De Gruyter
ISSN:1615-715X
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1515/advg.2002.002
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1895343
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0988.53033
http://front.math.ucdavis.edu/0102.5107 (Organisation)

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