View source for The induced fundamental group homomorphism of the identity map is the identity map of the fundamental group/Statement

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==Statement==
</noinclude>Let {{Top.|X|J}} be a [[topological space]], let {{M|\text{Id}_X:X\rightarrow X}} be the [[identity map]], given by {{M|\text{Id}_X:x\mapsto x}} and let {{M|p\in X}} be given (this will be the basepoint of [[the fundamental group|{{M|\pi_1(X,p)}}]]) then{{rITTMJML}}:
* the [[fundamental group homomorphism induced by a continuous map|induced map]] on [[the fundamental group]] {{M|\pi_1(X,p)}} is equal to the identity map on {{M|\pi_1(X,p)}}
** That is to say {{M|(\text{Id}_X)_*\eq\text{Id}_{\pi_1(X,p)}:\pi_1(X,p)\rightarrow\pi_1(X,p)}} where {{M|\text{Id}_{\pi_1(X,p)} }} is given by {{M|\text{Id}_{\pi_1(X,p)}:[f]\mapsto [f]}}<noinclude>
==References==
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{{Theorem Of|Algebraic Topology|Topology|Homotopy Theory}}
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