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Is the completion of a CAT(0) open ball a closed ball?

The answer is "no". Let $\Sigma$ be the suspension over Poincaré homology sphere. It admits a polyhedral $\mathrm{CAT}[1]$-metric. Let $B$ be the unit ball in the Euclidean cone $\mathrm{Cone}\,\Sig …
Anton Petrunin's user avatar