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

 

Tree-like continua and 2-to-1 maps


Authors: Jo Heath and Van C. Nall
Journal: Proc. Amer. Math. Soc. 132 (2004), 283-289
MSC (2000): Primary 54C10
Published electronically: August 19, 2003
MathSciNet review: 2021272
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Abstract: It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.


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Additional Information

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

Van C. Nall
Affiliation: Department of Mathematics & Computer Science, University of Richmond, Richmond, Virginia 23173
Email: vnall@richmond.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06989-2
PII: S 0002-9939(03)06989-2
Keywords: 2-to-1 map, tree-like continuum, dendroid, indecomposable continuum
Received by editor(s): November 16, 2001
Received by editor(s) in revised form: July 27, 2002
Published electronically: August 19, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society