  We consider time-delay systems with a finite number of delays in the state
space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward
completeness implies the bounded reachability sets property, while this
implication was recently shown by J.L. Mancilla-Aguilar and H. Haimovich to
fail in the state space of continuous functions. As a consequence, we show that
global asymptotic stability is always uniform in the state space
$L^\infty\times\mathbb{R}^n$.
