View source for Homeomorphic topological spaces have isomorphic fundamental groups/Statement

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==Statement==
</noinclude>Let {{Top.|X|J}} and {{Top.|Y|K}} be ''[[homeomorphic]]'' [[topological spaces]], let {{M|p\in X}} be given (this will be the base point of [[the fundamental group]] {{M|\pi_1(X,p)}}) and let {{M|\varphi:X\rightarrow Y}} be that homeomorphism. Then: {{rITTMJML}}:
* {{M|\pi_1(X,p)\cong\pi_1(Y,\varphi(p))}} - where {{M|\cong}} denotes [[group isomorphism]] here, but can also be used to denote [[topological isomorphism]] ({{AKA}}: [[homeomorphism]])
That is to say:
* {{M|\big(X\cong_\varphi Y)\implies(\pi_1(X,p)\cong_{\varphi_*}\pi_1(Y,\varphi(p))\big)}}<noinclude>
==References==
<references/>
{{Theorem Of|Topology|Algebraic Topology|Homotopy Theory}}
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