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Under appropriate regularity conditions it is shown that the continuous dependence of the global attractors $\mathcal{A}_\tau$ of semi dynamical systems $S^{(\tau)}(t)$ in $C([-\tau,0];Z)$ with $Z$ a Banach space and time delay $\tau \in [T_*,T^$*$]$, where $T_* > 0$, is equivalent to the equi-attraction of the attractors. Examples and counter examples posed in this right framework are provided.

Equi-Attraction and the continuous dependence of attractors on time delays