  Veech's Theorem claims that if $G$ is a locally compact\,(LC) Hausdorff
topological group, then it may act freely on $G^{\textrm{LUC}}$. We prove
Veech's Theorem for $G$ being only locally quasi-totally bounded, not
necessarily LC. And we show that the universal a.a. flow is the maximal almost
1-1 extension of the universal minimal a.p. flow and is unique up to almost 1-1
extensions. In particular, every endomorphism of Veech's hull flow induced by
an a.a. function is almost 1-1; for $G=\mathbb{Z}$ or $\mathbb{R}$, $G$ acts
freely on its canonical universal a.a. space. Finally, we characterize Bochner
a.a. functions on a LC group $G$ in terms of Bohr a.a. function on $G$ (due to
Veech 1965 for the special case that $G$ is abelian, LC, $\sigma$-compact, and
first countable).
