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

 

An uncountable family of copies of a non-chainable tree-like continuum in the plane


Author: L. C. Hoehn
Journal: Proc. Amer. Math. Soc. 141 (2013), 2543-2556
MSC (2010): Primary 54F15, 54F50
Published electronically: March 4, 2013
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Abstract: A well-known theorem of R. L. Moore states that the plane does not contain an uncountable family of pairwise disjoint triods. In 1974, Ingram demonstrated that the same is not true for non-chainable tree-like continua. The continua in Ingram's family are not pairwise homeomorphic, making the example less applicable to the study of homogeneous continua in the plane. In this paper, we construct a non-chainable tree-like continuum $ X$ such that the product of $ X$ with the Cantor set can be embedded in the plane.


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Additional Information

L. C. Hoehn
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
Address at time of publication: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, Box 5002, North Bay, Ontario, Canada P1B 8L7
Email: lhoehn@uab.edu, loganh@nipissingu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11760-0
PII: S 0002-9939(2013)11760-0
Keywords: Uncountable family, non-chainable, tree-like, continuum, plane
Received by editor(s): October 11, 2011
Published electronically: March 4, 2013
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.