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

 

Self-similarity in inverse limit spaces
of the tent family


Authors: Marcy Barge, Karen Brucks and Beverly Diamond
Journal: Proc. Amer. Math. Soc. 124 (1996), 3563-3570
MSC (1991): Primary 54F15, 58F03, 58F12
MathSciNet review: 1363409
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Abstract: Taking inverse limits of the one-parameter family of tent maps of the interval generates a one-parameter family of inverse limit spaces. We prove that, for a dense set of parameters, these spaces are locally, at most points, the product of a Cantor set and an arc. On the other hand, we show that there is a dense $G_\delta $ set of parameters for which the corresponding space has the property that each neighborhood in the space contains homeomorphic copies of every inverse limit of a tent map.


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Additional Information

Marcy Barge
Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
Email: barge@math.montana.edu

Karen Brucks
Affiliation: Department of Mathematical Sciences, University of Wisconsin at Milwaukee, Milwaukee, Wisconsin 53201
Email: kmbrucks@alpha1.csd.uwm.edu

Beverly Diamond
Affiliation: Department of Mathematics, University of Charleston, Charleston, South Carolina 29424
Email: diamondb@ashley.cofc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03690-8
PII: S 0002-9939(96)03690-8
Received by editor(s): May 16, 1995
Additional Notes: The first author was supported in part by NSF-DMS-9404145.
Communicated by: Mary Rees
Article copyright: © Copyright 1996 American Mathematical Society