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Let M be an indecomposable k-junctioned tree-like continuum. Let f be a map of M that sends each composant of M into itself. Using an argument of O. H. Hamilton, we prove that f has a fixed point. D. P. Bellamy  in 1979 defined a tree-like continuum that does not have the fixed-point property (also see , , , and ). In 1998, the author  proved that every tree-like continuum has the fixed-point property for deformations. This was accomplished by showing that every map of adoi:10.1090/s0002-9939-09-10165-x fatcat:oydnwu6qmffstfnmte7hwpy3ti