Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University 10.15672/hujms.464056 Mathematical Sciences Matematik On subgroup topologies on fundamental groups https://orcid.org/0000-0001-7222-3922 Rashid Mehdi Abdullahi Ferdowsi University of Mashhad https://orcid.org/0000-0002-3811-1721 Jamali Noorollah Ferdowsi University of Mashhad https://orcid.org/0000-0001-5243-0641 Mahsayekhy Behrooz Ferdowsi University of Mashhad https://orcid.org/0000-0001-7401-6599 Pashaei Seyyed Zeynal Ferdowsi University of Mashhad https://orcid.org/0000-0002-2609-4872 Torabı Hamid Ferdowsi University of Mashhad 06 02 2020 49 3 935 949 10 10 2018 05 20 2019 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

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.

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