论文标题
有限空间的警察和强盗
Cop and robber on finite spaces
论文作者
论文摘要
一个警察试图在拓扑空间中捕获强盗$ x $无法见到他。在哪个空间上，$ x $警察有一种策略，使他能够独立于逃脱的努力而占领强盗？换句话说，何时有曲线$γ：\ mathbb {r} _ {\ ge 0} \ to x $，它与$ x $中的任何其他曲线都一致。我们特别分析了有限拓扑空间的情况，并发现有关这些空间中路径的一般结果和外来示例。
A cop tries to capture a robber in a topological space $X$ being unable to see him. For which spaces $X$ does the cop have a strategy which allows him to capture the robber independently of his efforts to escape? In other words, when is there a curve $γ: \mathbb{R}_{\ge 0}\to X$ which has a coincidence with any other curve in $X$. We analyze in particular the case of finite topological spaces and discover general results and exotic examples about paths in these spaces.
