On two weaker forms of continuous order-homomorphisms

The aim of this paper is to find further connections between two different current researches on fuzzy topology: the one based on the concepts of neig hborhood, filter and Zadeh function, and the other based on the concepts of remote neighborhood, ideal and order-homomorphism on fuzzy lattices. To ap proach this, the paper studies two weaker forms of continuous order-homomor phisms, the semi-continuous order-homomorphism and the weakly semi-continuo us order-homomorphism between L-fuzzy topological spaces. These order-homom orphisms can be characterized in each of the notions: remote-neighborhood, neighborhood, ideal, filter and molecular net. In addition, some relations connecting weakly semi-continuous order-homomorphisms, semi-Hausdorff L-fts and Urysohn L-fts have also been established. (C) 1999 Elsevier Science B. V. All rights reserved.