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

 

A non-treelike continuum that is not
the 2-to-1 image of any continuum


Author: Jo W. Heath
Journal: Proc. Amer. Math. Soc. 124 (1996), 3571-3578
MSC (1991): Primary 54C10
MathSciNet review: 1371126
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Abstract: Some thirteen years ago S. B. Nadler, Jr. and L. E. Ward, Jr., asked if any treelike continuum could be the 2-to-1 image of a continuum. In fact, it has been conjectured that the property of being treelike characterizes those continua that are not the 2-to-1 image of any continuum. But the characterization must be something else; this paper shows that many pseudo-solenoids are not the 2-to-1 image of any continuum.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03735-5
PII: S 0002-9939(96)03735-5
Keywords: Pseudo-circle, pseudo-solenoid, 2-to-1 map, treelike continuum, indecomposable continuum, hereditarily indecomposable continuum
Received by editor(s): May 25, 1995
Communicated by: James E. West
Article copyright: © Copyright 1996 American Mathematical Society