On subgroup topologies on fundamental groups

Authors : Mehdi Abdullahi RASHİD, Noorollah JAMALİ, Behrooz MAHSAYEKHY, Seyyed Zeynal PASHAEİ, Hamid TORABI

Pages : 935-949

Doi:10.15672/hujms.464056

View : 23 | Download : 12

Publication Date : 2020-06-02

Article Type : Research Paper

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