Abstract. The paper is the last in the cycle devoted to the solution of Alexandrov’s problem for nonpositively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that if X is geodesically complete connected at infinity proper Busemann space, then it has the following characterization of isometries. For any bijection f: X → X, if f and f −1 preserve the distance 1, then f is an isometry
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