Title : ( On subgroup topologies on fundamental groups )
Authors: Mehdi Abdullahi Rashid , Noorollah Jamali , Behrooz Mashayekhy Fard , seyed zeynal pashaei , Hamid Torabi Ardakani ,
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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
@article{paperid:1078448,
author = {Abdullahi Rashid, Mehdi and Jamali, Noorollah and Mashayekhy Fard, Behrooz and Pashaei, Seyed Zeynal and Torabi Ardakani, Hamid},
title = {On subgroup topologies on fundamental groups},
journal = {Hacettepe Journal of Mathematics and Statistics},
year = {2019},
volume = {49},
number = {3},
month = {December},
issn = {1303-5010},
pages = {935--949},
numpages = {14},
keywords = {Semicovering; generalized covering; topological group; Spanier topology;
Whisker topology; Lasso topology; subgroup topology},
}
%0 Journal Article
%T On subgroup topologies on fundamental groups
%A Abdullahi Rashid, Mehdi
%A Jamali, Noorollah
%A Mashayekhy Fard, Behrooz
%A Pashaei, Seyed Zeynal
%A Torabi Ardakani, Hamid
%J Hacettepe Journal of Mathematics and Statistics
%@ 1303-5010
%D 2019
