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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

Van C. Nall
Affiliation: Department of Mathematics & Computer Science, University of Richmond, Richmond, Virginia 23173

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