Spaces of $\omega $-limit sets of graph maps
Volume 196 / 2007
Fundamenta Mathematicae 196 (2007), 91-100
MSC: Primary 37E25; Secondary 54B20.
DOI: 10.4064/fm196-1-2
Abstract
Let $(X,f)$ be a dynamical system. In general the set of all $\omega $-limit sets of $f$ is not closed in the hyperspace of closed subsets of $X$. In this paper we study the case when $X$ is a graph, and show that the family of $\omega $-limit sets of a graph map is closed with respect to the Hausdorff metric.
