Free deformation retraction in injective metric spaces (Q917965)

\textit{J. Isbell} proved that in every injective metric space X (with respect to contractions) each of its points is a free deformation retract of X [Comment. Math. Helv. 39, 65-76 (1964; Zbl 0151.302)]. The present authors generalize this result by replacing the points by the connected sets \(A\subset X\) having the property that \(A\cap \cap {\mathcal B}\neq \emptyset\) whenever the family (A)\(\cup {\mathcal B}\) is linked (each two members meet), and \({\mathcal B}\) is a family of closed balls in X.