Regular L-fuzzy topological spaces and their topological modifications

Abstract

For L a continuous lattice with its Scott topology, the functor ιL makes every regular L-topological space into a regular space and so does the functor ωL 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.