= Rationalization of a topological space
{title2=$r:X\to X_{\mathbb Q}$}
= Rationalisation of a topological space
{synonym}
For <simply connected> $X$, <rationalization of a topological space> is a map $r:X\to X_{\mathbb Q}$ to a <rational space> inducing $\pi_n(X_{\mathbb Q})=\pi_n(X)\otimes\mathbb Q$. It is also a <rational homology> equivalence. Its universal property is the bijection $r^*:[X_{\mathbb Q},Z]\to[X,Z]$ for every <rational space> $Z$. A <Postnikov tower> constructs it by replacing each fibre group with its rational <tensor product> and transporting the <Postnikov invariant> through the resulting <cohomology> isomorphism, then taking the <homotopy inverse limit>.
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