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Ramos-Cuevas, Carlos (2016): Convexity is a local property in CATκ(kappa) spaces. In: Bárcenas, Noé; Galaz-García, Fernando; Moreno Rocha, Mónica (eds.) : Mexican mathematicians abroad : recent contributions : First Workshop Matemáticos Mexicanos Jóvenes en el Mundo, August 22-24, 2012, Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico. Contemporary mathematics : CONM, Vol. 657. American Mathematical Society. pp. 189-196
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In this note we show that a connected, closed and locally convex subset (with an extra assumption on the diameter with respect to the induced length metric if kappa > 0) of a CAT(a) space is convex.