Let $��$ be a complete metric space, and let $\{S_��(\cdot):\ ��\in��\}$ be a parametrised family of semigroups with global attractors ${\mathscr A}_��$. We assume that there exists a fixed bounded set $D$ such that ${\mathscr A}_��\subset D$ for every $��\in��$. By viewing the attractors as the limit as $t\to\infty$ of the sets $S_��(t)D$, we give simple proofs of the equivalence of `equi-attraction' to continuity (when this convergence is uniform in $��$) and show that the attractors ${\mathscr A}_��$ are continuous in $��$ at a residual set of parameters in the sense of Baire Category (when the convergence is only pointwise).