Continuous mappings in soft lattice topological spaces

The fuzzy set, soft set and their extensions have proven to be a fruitful bridge between precise classical mathematics and the imprecise real world. Soft lattices, which are a generalization of soft sets, are a novel mathematical approach to the study of uncertainty. Soft lattice topological spaces are introduced over an initial universe X with a fixed set of parameters P. In this paper, we introduce the concept of soft lattice continuous mappings(soft L-continuous mappings) in soft lattice topological spaces which are defined with a fixed set of parameters over an initial universe. Further we investigate some properties regarding the continuity of mappings in soft lattice topological spaces. Finally, open mappings, closed mappings and homeomorphism on soft L-topological spaces are defined and some interesting results are obtained.