High Quality Content by WIKIPEDIA articles! In mathematics, a CAT(k) space is a specific type of metric space. Intuitively, triangles in a CAT(k) space are "slimmer" than corresponding "model triangles" in a standard space of constant curvature k. In a CAT(k) space, the curvature is bounded from above by k. A notable special case is k = 0: complete CAT(0) spaces are known as Hadamard spaces after the French mathematician Jacques Hadamard. The terminology "CAT(k)" was coined by Mikhail Gromov in 1987 and is an acronym for Elie Cartan, Aleksandr Danilovich Aleksandrov and Victor Andreevich Toponogov.

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