  Using the functor of Baumslag rationalization of groups we construct a
functor on the category of all (non necessarily simply connected) spaces that
extends the classical rationalization of simply connected spaces. We study this
functor and compare it with other extensions of the classical rationalization:
Bousfield-Kan $\mathbb Q$-completion; Bousfield's homology rationalization;
G\'{o}mez-Tato--Halperin--Tantr\'{e}'s $\pi_1$-fiberwise rationalization; and
the localization with respect to the maps $n:S^1\to S^1$ that we call
$\Omega$-rationalization.
