论文标题
同型距离引起的拓扑空间
Topological spaces induced by homotopic distance
论文作者
论文摘要
\ cite {mvml}中引入的同位距离$ \ d $可以在$ \ mathrm {map}（x，y）$上实现为伪计。在本文中，我们研究了假计$ \ d $引起的拓扑。特别是，我们考虑空间$ \ mathrm {map}（s^1，s^1）$ $，并证明该空间中任意两个地图之间的同型距离是1。
Homotopic distance $\D$ as introduced in \cite{MVML} can be realized as a pseudometric on $\mathrm{Map}(X,Y)$. In this paper, we study the topology induced by the pseudometric $\D$. In particular, we consider the space $\mathrm{Map}(S^1,S^1)$ and show that homotopic distance between any two maps in this space is 1. Moreover, while a general proof of the non-compactness of the space $\mathrm{Map}(X,Y)$ is still an open problem, it can be shown that $\mathrm{Map}(S^1,S^1)$ is not compact.
