EACH LOCALLY ONE-TO-ONE MAP FROM A CONTINUUM ONTO A TREE-LIKE CONTINUUM IS A HOMEOMORPHISM

In 1977 T. Mackowiak proved that each local homeomorphism from a conti nuum onto a tree-like continuum is a homeomorphism. Recently, J. Roger s proved that each locally one-to-one (not necessarily open) map from a hereditarily decomposable continuum onto a tree-like continuum is a homeomorphism, and this paper removes ''hereditarily decomposable'' fr om the hypothesis of Rogers' theorem.