Topology and its Applications, ( ISI ), Volume (254), Year (2019-3) , Pages (117-131)

Title : ( On strong small loop transfer spaces relative to subgroups of fundamental groups )

Authors: seyed zeynal pashaei , Behrooz Mashayekhy Fard , Hamid Torabi Ardakani , Mehdi Abdullahi Rashid ,

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Abstract

Let H be a subgroup of the fundamental group π1(X,x0). In this paper, first, we give a positive answer to a problem presented by Brodskiy et al. in [8, Problem 4.8]. Second, by extending the concept of strong SLT space to a relative version with respect to H, strong H-SLT space, we investigate the existence of a covering map for strong H-SLT spaces. Moreover, we show that a semicovering map is a covering map in the presence of strong H-SLT property. Among other things, we present conditions under which the whisker topology agrees with the lasso topology on X˜H. Also, we study the relationship between open subsets of π1wh(X,x0) and π1l(X,x0). Finally, we give several examples to justify the definition and study of strong H-SLT spaces when H is a non-trivial subgroup.

Keywords

, Strong small loop transfer space, Quasitopological fundamental group, Whisker topology, Lasso topology, Covering map, Semicovering map
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@article{paperid:1076058,
author = {Pashaei, Seyed Zeynal and Mashayekhy Fard, Behrooz and Torabi Ardakani, Hamid and Abdullahi Rashid, Mehdi},
title = {On strong small loop transfer spaces relative to subgroups of fundamental groups},
journal = {Topology and its Applications},
year = {2019},
volume = {254},
month = {March},
issn = {0166-8641},
pages = {117--131},
numpages = {14},
keywords = {Strong small loop transfer space; Quasitopological fundamental group; Whisker topology; Lasso topology; Covering map; Semicovering map},
}

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%0 Journal Article
%T On strong small loop transfer spaces relative to subgroups of fundamental groups
%A Pashaei, Seyed Zeynal
%A Mashayekhy Fard, Behrooz
%A Torabi Ardakani, Hamid
%A Abdullahi Rashid, Mehdi
%J Topology and its Applications
%@ 0166-8641
%D 2019

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