- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- On subgroup topologies on fundamental groups
On subgroup topologies on fundamental groups
Authors : Mehdi Abdullahi Rashid, Noorollah Jamali, Behrooz Mahsayekhy, Seyyed Zeynal Pashaei, Hamid Torabi
Pages : 935-949
Doi:10.15672/hujms.464056
View : 13 | Download : 5
Publication Date : 2020-06-02
Article Type : Research
Abstract :It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental group and use them to classify coverings, semicoverings, and generalized coverings of a topological space. To do this, we use the concept of subgroup topology on a group and discuss their properties. In particular, we explore which of these topologies make the fundamental group a topological group. Moreover, we provide some examples of topological spaces to compare topologies of fundamental groups.Keywords : Semicovering, Generalized covering, Topological group, Spanier topology, Whisker topology, Lasso topology, Subgroup topology