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 | References | Similar Articles | Additional Information
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.
- 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
