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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

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The n-Point Condition and Rough CAT(0)

Stephen M. Buckley / Bruce Hanson
  • Department of Mathematics, Statistics and Computer Science, St. Olaf College, 1520 St. Olaf Avenue, Northfield, MN 55057, USA
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Published Online: 2013-01-14 | DOI: https://doi.org/10.2478/agms-2012-0005


We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.

Keywords: CAT(0) space; rough CAT(0) space; Gromov hyperbolic space; Gromov-Hausdorff limit; ultralimit

MSC: 30L05; 51M05

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About the article

Received: 2012-10-24

Accepted: 2012-12-24

Published Online: 2013-01-14

Citation Information: Analysis and Geometry in Metric Spaces, Volume 1, Pages 58–68, ISSN (Online) 2299-3274, DOI: https://doi.org/10.2478/agms-2012-0005.

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©2012 Versita Sp. z o.o.. This content is open access.

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