A dense subgroup of topological fundamental groups of quotient spaces

Details A dense subgroup of topological fundamental groups of quotient spaces A dense subgroup of topological fundamental groups of quotient spaces

2011-05-20

arxiv.org/abs/1105.4009v1

Mathematics

Algebraic Topology

10 pages, 1 figure

Scientific paper

In this paper, we show that the image of the topological fundamental group of a given space $X$ is dense in the topological fundamental group of the quotient space $X/A$ under the induced homomorphism of the quotient map, where $A$ is a suitable subspace of $X$ with some conditions on $X$. Also, we give some application to find out some properties for $\pi_1^{top}(X/A,*)$. In particular, we give some condition in which $\pi_1^{top}(X/A,*)$ is an indiscrete topological group.

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