We investigate the geometry of spaces tangent and pretangent to general metric spaces with marked point. We find a sufficient condition under which every separable tangent space is geodesic. This condition is almost exact in the sense that it is necessarily satisfied if all spaces pretangent to a given metric space are geodesic.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1273–1281, September, 2012.
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Bilet, V.V. Geodesic spaces tangent to metric spaces. Ukr Math J 64, 1448–1456 (2013). https://doi.org/10.1007/s11253-013-0727-4
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DOI: https://doi.org/10.1007/s11253-013-0727-4