  In this paper, for a full subcategory $\mathbf{K}$ of the category of all
$T_0$ spaces with continuous mappings, we investigate the questions under what
conditions the $\mathbf{K}$-reflection of a Scott space is still a Scott space
and under what conditions the Scott $\mathbf{K}$-completion of a poset exists.
Some necessary and sufficient conditions for the $\mathbf{K}$-reflection of a
Scott space to be a Scott space and for the existence of Scott
$\mathbf{K}$-completion of a poset are established, respectively. It is shown
that neither the sobrification nor the well-filtered reflection of the
Johnstone space is a Scott space. The $\mathbf{K}$-reflections of Alexandroff
spaces and the $\mathbf{K}$-completions of posets are also discussed.
