Abstract:
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.
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