Local convexity in CAT(kappa)-spaces
classification
🧮 math.MG
keywords
spacesconvexeuclideankappalocalapplicationbuildingscertain
read the original abstract
Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a local property. We generalize this to CAT(0)-spaces and locally compact CAT(\kappa) spaces. As an application we give a construction of certain convex sets in euclidean buildings.
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