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.
@article{bwmeta1.element.doi-10_2478_agms-2012-0005, author = {Stephen M. Buckley and Bruce Hanson}, title = { The n -Point Condition and Rough CAT(0) }, journal = {Analysis and Geometry in Metric Spaces}, volume = {1}, year = {2013}, pages = {58-68}, zbl = {1262.30073}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_agms-2012-0005} }
Stephen M. Buckley; Bruce Hanson. The n -Point Condition and Rough CAT(0) . Analysis and Geometry in Metric Spaces, Tome 1 (2013) pp. 58-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_agms-2012-0005/
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