International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 687-695
Regular -fuzzy topological spaces and their topological modifications
1Wydzial Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, Matejki, 48/49, Poznań 60–769, Poland
2Departamento de Matemáticas, Universidad del País Vasco - Euskal Herriko Unibertsitatea, Apdo. 644, Bilbao 48080, Spain
Copyright © 2000 T. Kubiak and M. A. de Prada Vicente. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For a continuous lattice with its Scott topology, the functor
makes every regular -topological space into a regular
space and so does the functor 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
-Lindelöfness (á la Hutton compactness) is introduced
and characterized in terms of certain filters. Regular
-Lindelöf spaces are shown to be normal.