Title : ( On Topologized Fundamental Groups with Small Loop Transfer Viewpoints )
Authors: Noorollah Jamali , Behrooz Mashayekhy Fard , Hamid Torabi Ardakani , seyed zeynal pashaei , Mehdi Abdullahi Rashid ,
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Abstract
In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology, $\pi_{1}^{qtop}(X,x_{0})$ and $\pi_{1}^{wh}(X,x_{0})$, respectively. In particular, we give necessary or sufficient conditions for equality and being topological group of these two topologized fundamental groups. Finally, we give some examples to show that the converse of some of these implications do not hold, in general.
Keywords
, Small loop transfer space, quasitopological fundamental group, whisker topology, topological group.
@article{paperid:1067197,
author = {Jamali, Noorollah and Mashayekhy Fard, Behrooz and Torabi Ardakani, Hamid and Pashaei, Seyed Zeynal and Abdullahi Rashid, Mehdi},
title = {On Topologized Fundamental Groups with Small Loop Transfer Viewpoints},
journal = {Acta Mathematica Vietnamica},
year = {2018},
volume = {43},
number = {4},
month = {December},
issn = {0251-4184},
pages = {1--27},
numpages = {26},
keywords = {Small loop transfer space; quasitopological fundamental group; whisker topology; topological group.},
}
%0 Journal Article
%T On Topologized Fundamental Groups with Small Loop Transfer Viewpoints
%A Jamali, Noorollah
%A Mashayekhy Fard, Behrooz
%A Torabi Ardakani, Hamid
%A Pashaei, Seyed Zeynal
%A Abdullahi Rashid, Mehdi
%J Acta Mathematica Vietnamica
%@ 0251-4184
%D 2018
