无边界曲面上同胚群的紧开拓扑是极小的
几何拓扑
2022-11-08 v3 一般拓扑
摘要
我们证明无边界曲面的同胚群不承认严格粗于紧开拓扑的Hausdorff群拓扑。结合已知的自动连续性结果，这意味着若该曲面是闭曲面，或是闭曲面中去掉有限集、或有限集与Cantor集之并后的补集，则紧开拓扑是该群上唯一的Hausdorff可分离群拓扑。
引用
@article{arxiv.2210.17280,
title = {The compact-open topology on the homeomorphism group of a surface without boundary is minimal},
author = {J. de la Nuez González},
journal= {arXiv preprint arXiv:2210.17280},
year = {2022}
}
备注
15 pages, Lemma 3.6 has been corrected. The argument why K\union L was contained in the closure of U_0 was faulty