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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03736-7
PII: S 0002-9939(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