# rationalization space

let $X$ be a topological space and $X_\mathbb Q$ its rationalization.

1) what is the rationalization of $X_\mathbb Q$, is it $X_\mathbb Q$ itself?

2) if $X$ is a CW complex, does that imply necesserely that $X_\mathbb Q$ is a CW complex

3) if $X_\mathbb Q$ and $X'_\mathbb Q$ are two rationalizations of $X$, how do they relate, my guess is that they are weakly equivalent and so if they are CW complexes they are homotopy equivalent.

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Given that rationalization is defined by a universal property, certainly $(X_\mathbb{Q})_\mathbb{Q}\cong X_{\mathbb{Q}}$. –  Aaron Mazel-Gee May 10 '11 at 20:01