Homotopy Group is Homeomorphism Invariant

= Theorem =

Given two manifolds $$X$$ and $$Y$$, if there is a homeomorphism $$f:X \to Y$$, then $$\forall n \in \mathbb{N}, \pi_n(X) = \pi_n(Y)$$, where the $$\pi_n$$ are the $$n^{th}$$ homotopy groups.

= Proof =