论文标题
$ \ mathbb {r}^n $的紧凑子集的超级空间的路径连接性
Path-Connectedness of the Hyperspace of Compact Subsets of $\mathbb{R}^n$
论文作者
论文摘要
当人们考虑$ \ mathcal {h}（\ mathbb {r}^n）$的所有紧凑型子集的$ \ mathbb {r}^n $并配备拓扑时，可以问许多有关拓扑空间的问题。这是一个超级空间的例子，这是一个数学对象，自20世纪初以来，它已经在更抽象的环境中进行了研究。在这里，我们给出了$ \ Mathcal {h}（\ Mathbb {r}^n）$的路径连接性的基本证明，并通过Hausdoff Metric引起的拓扑结构来探索$ \ Mathbb {r}^n $的矢量结构，并且仅利用与知识学生的基础知识相关的基础学的基础，并且只能使用概念的学生来理解这些知识的基础。
When one considers the collection $\mathcal{H}(\mathbb{R}^n)$ of all compact subsets of $\mathbb{R}^n$ and equip it with a topology, many questions can be asked about the topological space one ends up with. This is an example of a hyperspace, a mathematical object which has been studied in a more abstract setting since the beginning of the 20th century. Here we give an elementary proof of the path-connectedness of $\mathcal{H}(\mathbb{R}^n)$, with the topology induced by the Hausdoff metric, by exploring the vector structure of $\mathbb{R}^n$ and using only basic ideas of topology of metric spaces that undergraduate students with just a basic knowledge of these concepts will be able to understand.
