# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Hereditarily indecomposable inverse limits of graphs

### Tom 185 / 2005

Fundamenta Mathematicae 185 (2005), 195-210 MSC: 54F15, 54H20. DOI: 10.4064/fm185-3-1

#### Streszczenie

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.

#### Autorzy

• K. KawamuraInstitute of Mathematics
University of Tsukuba
Tsukuba, Ibaraki 305-8571, Japan
e-mail
• H. M. TuncaliFaculty of Arts and Science
Nipissing University
100 College Drive, Box 5002
North Bay, Ontario
e-mail
• E. D. TymchatynDepartment of Mathematics and Statistics