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In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s $4$ -point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.
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You et al. (2024) studied this question.
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