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Hereditarily indecomposable inverse limits of graphs

K. Kawamura; H. M. Tuncali; E. D. Tymchatyn — 2005

Fundamenta Mathematicae

We prove the following theorem: Let G be a compact connected graph and let f: G → 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 fⁿ(A) = G. Then, for each ε > 0, there is a map $f_{ε} : G \to G$ which is ε-close to f such that the inverse limit $(G, f_{ε})$ is hereditarily indecomposable.

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