Topological fundamental groupoids: Brown`s topology

Authors : Ali PAKDAMAN, Fereshteh SHAHİNİ

Pages : 896-906

Doi:10.15672/hujms.1205441

View : 190 | Download : 248

Publication Date : 2023-08-15

Article Type : Research Paper

Abstract :In this paper, we generalize the Brown$^{^,}$s topology on the fundamental groupoids. For a locally path connected space $X$ and a totally disconnected normal subgroupoid $M$ of $\\pi X$, we define a topology on the quotient groupoid $\\dfrac{\\pi X}{M}$ which is a generalization of what introduced by Brown for locally path connected and semilocally simply connected spaces. We prove that $\\dfrac{\\pi X}{M}$ equipped with this topology is a topological groupoid. Also, we will find a class of subgroupoids of topological groupoids whose their related quotient groupoids will be topological groupoids. By using this, we show that our topology on $\\dfrac{\\pi X}{M}$ is equivalent to the quotient of the Lasso topology on the topological fundamental groupoids, $\\dfrac{\\pi^L X}{M}$.
Keywords : fundamental groupoid‎, ‎topological groupoid‎, ‎quotient groupoid