Hereditarily indecomposable inverse limits of graphs
Volume 185 / 2005
Fundamenta Mathematicae 185 (2005), 195-210
MSC: 54F15, 54H20.
DOI: 10.4064/fm185-3-1
Abstract
We prove the following theorem: Let $G$ be a compact connected graph and let $f:G\rightarrow G$ be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum $A$ of $G$, there is a positive integer $n$ such that $f^n (A) = G.$ Then, for each $\varepsilon >0$, there is a map ${f_\varepsilon}:G \rightarrow G$ which is $\varepsilon$-close to $f$ such that the inverse limit $(G, f_\varepsilon)$ is hereditarily indecomposable.
