Geodesic spaces tangent to metric spaces - Bilet, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
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.