标题： 基本群上的拓扑比较与子群拓扑视角 显示英文标题

标题： Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint

摘要： 为了使基本群这一代数拓扑中最著名的不变量更加有用和强大，一些研究人员从21世纪初开始引入并研究了基本群上的各种拓扑。 在本文中，通过回顾这些拓扑，利用子群拓扑的概念，我们将比较这些拓扑，以提出一些关于拓扑化基本群的结果。 显示英文摘要

摘要： In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the 21st century onwards. In this paper by reviewing these topologies, using the concept of subgroup topology, we are going to compare these topologies in order to present some results on topologized fundamental groups.