On the Topologies of Injective Spaces

This paper presents a characterization of the lattices of open sets of injective T₀-spaces, and thus of the Scott topologies of continuous lattices (Scott [10]; see also Compendium [3], 2), in purely lattice theoretic terms, i.e., by conditions involving only the join and meet operations of the lattice. We remark that this differs conceptually from the earlier characterization in Banaschewski [2] which employs completely prime filters.