| Citation: |
Risong Li, Tianxiu Lu, Weizhen Quan, Jingmin Pi. A NOTE ON TOPOLOGICALLY TRANSITIVE TREE MAPS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1801-1815. doi: 10.11948/20210354
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A NOTE ON TOPOLOGICALLY TRANSITIVE TREE MAPS
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Abstract
In this note, $ W $ is a tree. $ F: W\rightarrow W $ is a continuous map. $ \mathcal{K}(W)=\{C\subset W: C\neq\emptyset $ and $ C $ is compact$ \} $ is endowed with a Hausdorff metric. The paper gives a sufficient and necessary condition under which $ F $ is topologically transitive. Furthermore, it is shown that both a topologically transitive tree map $ F: W\rightarrow W $ and the continuous map $ \overline{F} $ on $ \mathcal{K}(W) $ which is induced by $ F $ are cofinitely sensitive, where $ \overline{F}(C)=\{F(x):x\in C\} $ for any $ C\in \mathcal{K}(W) $.
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References
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Risong Li, Tianxiu Lu, Weizhen Quan, Jingmin Pi. A NOTE ON TOPOLOGICALLY TRANSITIVE TREE MAPS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1801-1815. doi: 10.11948/20210354
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