Baumslag rationalization of spaces

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.