Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Each locally one-to-one map from a continuum onto a tree-like continuum is a homeomorphism

Author(s): Jo W. Heath
Journal: Proc. Amer. Math. Soc. 124 (1996), 2571-2573.
MSC (1991): Primary 54C10
MathSciNet review: 1371127
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Abstract: In 1977 T. Mackowiak proved that each local homeomorphism from a continuum onto a tree-like continuum is a homeomorphism. Recently, J. Rogers 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" from the hypothesis of Rogers' theorem.

References:

1.: James T. Rogers, Jr., Diophantine conditions imply critical points on the boundaries of Siegel disks of polynomials I, Preprint.
2.: James T. Rogers, Jr., Critical points on the boundaries of Siegel disks, Bull. Amer. Math. Soc. (N.S.) 32 (1995), 317--321. MR 96a:30032
3.: T. Mackowiak, Local homeomorphisms onto tree-like continua, Colloq. Math. XXXVIII (1977), 63--68. MR 57:4135

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