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


Author: Jo W. Heath
Journal: Proc. Amer. Math. Soc. 124 (1996), 2571-2573
MSC (1991): Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-96-03736-7
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 [Enhancements On Off] (What's this?)

  • 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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Additional Information

Jo W. Heath
Affiliation: Department of Mathematics, Auburn University, Alabama 36849-5310
Email: heathjw@mail.auburn.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03736-7
Keywords: Tree-like, locally one-to-one, chain, tree-indexing, continuum
Received by editor(s): January 30, 1995
Communicated by: James West
Article copyright: © Copyright 1996 American Mathematical Society

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