关于有限空间的映射类群的注记

摘要：

研究了一类包含有限空间的非Hausdorff拓扑空间的映射类群.证明了有限空间的映射类群同构于其$T_0$商的同胚群。作为推论，我们证明了每个有限群都是某个有限$T_0$空间的映射类群。

英文摘要：

We investigate the mapping class groups of a class of non-Hausdorff topological spaces which includes finite spaces. We show that the mapping class group of a finite space is isomorphic to the homeomorphism group of its $T_0$ quotient. As a corollary, we show that every finite group is the mapping class group of some finite, $T_0$ space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。