ABSTRACT
The purpose of this chapter is to demonstrate how group theory is applied in a different mathematical discipline, namely topology, to obtain substantial results in that discipline. The procedure of translating topological problems into group-theoretical problems will be as follows. To each topological space X we assign a group F(X), and to each continuous mapping f : X → Y we assign a group homomorphism F(f): F(X) → F(Y) such that the following conditions hold: ( 1 ) F ( id X ) = id F ( X ) ; ( 2 ) F ( f ∘ g ) = F ( f ) ∘ F ( g ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136547/a57ae1f0-6f59-46bd-bbdd-35a521b486a1/content/eq3492.tif"/>
