Each locally one-to-one map from a continuum onto a tree-like continuum is a homeomorphism
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- by Jo W. Heath PDF
- Proc. Amer. Math. Soc. 124 (1996), 2571-2573 Request permission
Abstract:
In 1977 T. Maćkowiak 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
- James T. Rogers, Jr., Diophantine conditions imply critical points on the boundaries of Siegel disks of polynomials I, Preprint.
- James T. Rogers Jr., Critical points on the boundaries of Siegel disks, Bull. Amer. Math. Soc. (N.S.) 32 (1995), no. 3, 317–321. MR 1316499, DOI 10.1090/S0273-0979-1995-00600-2
- T. Maćkowiak, Local homeomorphisms onto tree-like continua, Colloq. Math. 38 (1977), no. 1, 63–68. MR 464200, DOI 10.4064/cm-38-1-63-68
Additional Information
- Jo W. Heath
- Affiliation: Department of Mathematics, Auburn University, Alabama 36849-5310
- Email: heathjw@mail.auburn.edu
- Received by editor(s): January 30, 1995
- Communicated by: James West
- © Copyright 1996 American Mathematical Society
- 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