Ukrainian Mathematical Journal, Volume (65), No (12), Year (2014-12) , Pages (1883-1897)

Title : ( On topological fundamental groups of quotient spaces )

Authors: Hamid Torabi Ardakani , Ali Pakdaman , Behrooz Mashayekhy Fard ,

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Abstract

Let $p:X\rightarrow X/A$ be a quotient map, where $A$ is a subspace of $X$. We explore conditions under which $p_*(\pi_1^{qtop}(X,x_0))$ is dense in $\pi_1^{qtop}(X/A,*))$, where the fundamental groups enjoy the natural quotient topology inherited from the loop space and $p_*$ is the induced continuous homomorphism by the quotient map $p$. Also, we give some applications to find out some properties for $\pi_1^{qtop}(X/A,*)$. In particular, we give some conditions in which $\pi_1^{qtop}(X/A,*)$ is an indiscrete topological group.

Keywords

, Topological fundamental group, Quasitopological fundamental group, Quotient map, Dense subgroup
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@article{paperid:1042492,
author = {Torabi Ardakani, Hamid and Ali Pakdaman and Mashayekhy Fard, Behrooz},
title = {On topological fundamental groups of quotient spaces},
journal = {Ukrainian Mathematical Journal},
year = {2014},
volume = {65},
number = {12},
month = {December},
issn = {0041-5995},
pages = {1883--1897},
numpages = {14},
keywords = {Topological fundamental group; Quasitopological fundamental group; Quotient map; Dense subgroup},
}