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Oct 24, 2014 at 16:58 comment added Włodzimierz Holsztyński Thank you @Tom. Isbell's paper is a well known classic. Of course the equivalence of the ball binary property, metric injectivity and metric absolute retract property is a very simple property (even if it can be formulated as a theorem, why not). Of course being a an absolute (topological) retract among the metrisable spaces is more general than being homeomorphic to an injective metric space (even among the separable metric spaces, or even among finite polyhedra) these two notions are not equivalent.
Oct 24, 2014 at 15:48 history answered Tom Leinster CC BY-SA 3.0