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The Boundary at Infinity of a Rough CAT(0) Space

S.M. Buckley, K. Falk (2014)

Analysis and Geometry in Metric Spaces

We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic length space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper

The n -Point Condition and Rough CAT(0)

Stephen M. Buckley, Bruce Hanson (2013)

Analysis and Geometry in Metric Spaces

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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