Some modifications of Scott's theorem on injective spaces (Q1088182)

A well-known theorem of \textit{D. S. Scott} [Toposes, Algebraic Geometry and Logic, Dalhousie Univ. Halifax 1971, Lect. Notes Math. 274, 97-136 (1976; Zbl 0239.54006)] characterizes the injectives (absolute extensors) in the category of \(T_ 0\) topological spaces as the spaces obtained by endowing continuous lattices with the Scott-topology. The author extends Scott's theorem to categories of (\(\alpha\),\(\delta)\)-closure spaces, where \(\alpha\) and \(\delta\) are cardinals (Scott's theorem being the particular case \(\alpha =\omega\), \(\delta =\infty)\).