$\mathbb R$-factorizability of $G$-spaces in the category G-Tych

We introduce and characterize the notion of $\mathbb R$-factorizability of $G$-spaces in the category G-Tych. For $G$-spaces with $d$-openly acting groups, we establish the equivalence of $\mathbb R$-factorizability and $\mathbb R$-factorizability in G-Tych. We prove the $\mathbb R$-factorizability in G-Tych of every $\mathbb R$-factorizable $G$-space with transitive action whose phase space possesses the Baire property. The Dieudonné completion of an $\mathbb R$-factorizable group is shown to be the phase space of a $G$-space $\mathbb R$-factorizable in G-Tych. We characterize $\mathbb R$-factorizability in G-Tych under passage to the $G$-compactification.