I am looking for a reference or a proof of the following fact:

Let $X_{1}\subset X_{2}\subset\dots $ be a sequence of (hausdorff) topological spaces indexed by natural numbers such that each $X_{i}\subset X_{i+1}$ is a closed subspace for any $i\in \mathbb{N}$. We define $X=colim_{i\in \mathbb{N}}X_{i}$.

Then the $H_{m}(X,\mathbb{Z})=colim_{i\in \mathbb{N}}H_{m}(X_{i},\mathbb{Z})$ for any natural number $m\in\mathbb{N}$.