Title : ( On locally 1-connectedness of quotient spaces and its applications to fundamental groups )
Authors: Ali Pakdaman , Hamid Torabi Ardakani , Behrooz Mashayekhy Fard ,
Full TextAbstract
Let $X$ be a locally 1-connected metric space and $A_1,A_2,...,A_n$ be connected, locally path connected and compact pairwise disjoint subspaces of $X$. In this paper, we show that the quotient space $X/(A_1,A_2,...,A_n)$ obtained from $X$ by collapsing each of the sets $A_i$'s to a point, is also locally 1-connected. Moreover, we prove that the induced continuous homomorphism of quasitopological fundamental groups is surjective. Finally, we give some applications to find out some properties of the fundamental group of the quotient space $X/(A_1,A_2,...,A_n)$.
Keywords
, Locally 1-connected, Quotient space, Quasitopological fundamental group
@article{paperid:1039971,
author = {Ali Pakdaman and Torabi Ardakani, Hamid and Mashayekhy Fard, Behrooz},
title = {On locally 1-connectedness of quotient spaces and its applications to fundamental groups},
journal = {Filomat},
year = {2014},
volume = {28},
number = {1},
month = {January},
issn = {0354-5180},
pages = {27--35},
numpages = {8},
keywords = {Locally 1-connected; Quotient space; Quasitopological fundamental group},
}
%0 Journal Article
%T On locally 1-connectedness of quotient spaces and its applications to fundamental groups
%A Ali Pakdaman
%A Torabi Ardakani, Hamid
%A Mashayekhy Fard, Behrooz
%J Filomat
%@ 0354-5180
%D 2014
