Title : ( On Topologized Fundamental Groups and Covering Groups of Topological Groups )
Authors: Hamid Torabi Ardakani ,
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Abstract
We show that every topological group is a strong small loop transfer space at the identity element. This implies that for a connected locally path connected topological group G, the universal path space Gee equipped with the quotient topology induced by the compact-open topology on P(G, e) is a topological group. Moreover, we prove that there is a one-to-one correspondence between the equivalence classes of connected covering groups of G and the subgroups of p1ðG; eÞ that contain iðp1ðU; eÞÞ for some open neighborhood U of the identity element e
Keywords
Topological group Quasitopological fundamental group Covering map
@article{paperid:1083377,
author = {Torabi Ardakani, Hamid},
title = {On Topologized Fundamental Groups and Covering Groups of Topological Groups},
journal = {Iranian Journal of Science and Technology-Transaction A: Science},
year = {2020},
volume = {44},
number = {6},
month = {December},
issn = {1028-6276},
pages = {1731--1737},
numpages = {6},
keywords = {Topological group Quasitopological fundamental group Covering map},
}
%0 Journal Article
%T On Topologized Fundamental Groups and Covering Groups of Topological Groups
%A Torabi Ardakani, Hamid
%J Iranian Journal of Science and Technology-Transaction A: Science
%@ 1028-6276
%D 2020
