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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Universal maps on trees


Authors: Carl Eberhart and J. B. Fugate
Journal: Trans. Amer. Math. Soc. 350 (1998), 4235-4251
MSC (1991): Primary 54H25; Secondary 54F20
DOI: https://doi.org/10.1090/S0002-9947-98-02026-1
MathSciNet review: 1443871
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Abstract: A map $f:R \to S$ of continua $R$ and $S$ is called a universal map from $R$ to $S$ if for any map $g:R \to S$, $f(x) = g(x)$ for some point $x \in R$. When $R$ and $S$ are trees, we characterize universal maps by reducing to the case of light minimal universal maps. The characterization uses the notions of combinatorial map and folded subedge of $R$.


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Additional Information

Carl Eberhart
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: carl@ms.uky.edu

J. B. Fugate
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: fugate@ms.uky.edu

DOI: https://doi.org/10.1090/S0002-9947-98-02026-1
Keywords: Minimal universal, combinatorial, tree, fixed point property
Received by editor(s): May 5, 1987
Received by editor(s) in revised form: January 21, 1997
Article copyright: © Copyright 1998 American Mathematical Society