Universal maps on trees

Eberhart, Carl; Fugate, J.

doi:10.1090/S0002-9947-98-02026-1

Universal maps on trees
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by Carl Eberhart and J. B. Fugate PDF

Trans. Amer. Math. Soc. 350 (1998), 4235-4251 Request permission

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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