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Martin Sleziak
Martin Sleziak
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With the following additional assumptions: $K$ is compact, connected and locally convex, then it is proved in https://arxiv.org/pdf/1304.4147.pdf that $K$ is convex (Theorem 1.1). In this case, $co(K)=K$ is compact.

Carlos Ramos-Cuevas: Convexity is a local property in CAT(κ) spaces, arXiv:1304.4147

With the following additional assumptions: $K$ is compact, connected and locally convex, then it is proved in https://arxiv.org/pdf/1304.4147.pdf that $K$ is convex (Theorem 1.1). In this case, $co(K)=K$ is compact.

With the following additional assumptions: $K$ is compact, connected and locally convex, then it is proved in https://arxiv.org/pdf/1304.4147.pdf that $K$ is convex (Theorem 1.1). In this case, $co(K)=K$ is compact.

Carlos Ramos-Cuevas: Convexity is a local property in CAT(κ) spaces, arXiv:1304.4147

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MaJ
MaJ
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With the following additional assumptions: $K$ is compact, connected and locally convex, then it is proved in https://arxiv.org/pdf/1304.4147.pdf that $K$ is convex (Theorem 1.1). In this case, $co(K)=K$ is compact.