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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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Convex hull in CAT(0)
There is a counterexample if instead of the CAT(0) condition a weaker notion of non-positive curvature is considered. A bicombing on a metric space distinguishes for each pair of points a geodesic con …