Hereditarily indecomposable inverse limits of graphs

Volume 185 / 2005

K. Kawamura, H. M. Tuncali, E. D. Tymchatyn Fundamenta Mathematicae 185 (2005), 195-210 MSC: 54F15, 54H20. DOI: 10.4064/fm185-3-1


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.


  • K. KawamuraInstitute of Mathematics
    University of Tsukuba
    Tsukuba, Ibaraki 305-8571, Japan
  • H. M. TuncaliFaculty of Arts and Science
    Nipissing University
    100 College Drive, Box 5002
    North Bay, Ontario
    Canada P1B 8L7
  • E. D. TymchatynDepartment of Mathematics and Statistics
    University of Saskatchewan
    106 Wiggins Road
    Saskatoon, Saskatchewan
    Canada S7N 5E6

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