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Convergence of subsets of a complete geodesic space with curvature bounded above. (English) Zbl 1243.49054

Summary: We consider a notion of set-convergence in a Hadamard space recently defined by Kimura and extend it to that in a complete geodesic space with curvature bounded above by a positive number. We obtain its equivalent condition by using the corresponding sequence of metric projections. We also discuss the Kadec–Klee property on such spaces and interaction among this set-convergence having different curvatures.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
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