For L a continuous lattice with its Scott topology, the functor ι L makes every regular L -topological space into a regular space and so does the functor ω L the other way around. This has previously been known to hold in the restrictive class of the so-called weakly induced spaces. The concepts of H -Lindelöfness (á la Hutton compactness) is introduced and characterized in terms of certain filters. Regular H -Lindelöf spaces are shown to be normal.