Lattice-valued Semicontinuous Mappings and Induced Topologies

Lattice-valued semicontinuous mappings play a basic and important role in solvingthe problems of L-fuzzy compactification theory,and make the previous work on weakly inducedspaces and induced spaces determinatively generalized and strengthened.Moreover,we can describethe complete distributivity of lattices with them as well.In this paper,we give the mutually descrip-tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices,and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces,weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi-gate the structure of the co-topology of S-space,solve a series of interesting problems on product,N-compactness and metrization of S-spaces.