Spaces of w-limit sets of graph maps
Spaces of w-limit sets of graph maps
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DOI：
10.4064/fm196-1-2
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发表时间：
2007
影响因子：
0.6
通讯作者：
J. Mai;S. Shao
中科院分区：
文献类型：
--
作者：
J. Mai;S. Shao
设$(X,f)$为一个动力系统。一般来说，$f$的所有$\omega$-极限集构成的集合在$X$的闭子集的超空间中不是闭的。在本文中，我们研究当$X$是一个图的情形，并证明一个图映射的$\omega$-极限集族关于豪斯多夫度量是闭的。
Let (X, f) be a dynamical system. In general the set of all ω-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 ω-limit sets of a graph map is closed with respect to the Hausdorff metric.