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A homeomorphism h: X → X is called expansive provided that for some fixed c > 0 and every x, y ∈ X there exists an integer n, dependent only on x and y, such that d(h n (x), h n (y)) > c. It is shown that if X is a tree-like continuum, then h cannot be expansive.

Tree-like continua do not admit expansive homeomorphisms