The n-Point Condition and Rough CAT(0)

Stephen M. Buckley 1  and Bruce Hanson 2
  • 1 Department of Mathematics and Statistics, National University of Ireland Maynooth, Maynooth, Co. KIldare, Ireland
  • 2 Department of Mathematics, Statistics and Computer Science, St. Olaf College, 1520 St. Olaf Avenue, Northfield, MN 55057, USA


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.

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Analysis and Geometry in Metric Spaces (AGMS) is a fully peer-reviewed, open access electronic journal that publishes cutting-edge original research on analytical and geometrical problems in metric spaces and their mathematical applications. It features articles making connections among relevant topics in this field.