Lattice-valued induced fuzzy topological spaces

The aim of this paper is to study induced LM-fuzzy topological spaces. Firstly, we study the stratifications of LM-fuzzy topologies and show that SLM-FTOP—the category of stratified LM-fuzzy topological spaces—is a coreflective full subcategory of LM-FTOP. Secondly, we study Kubiak–Lowen functors ω and ι in LM-fuzzy topological spaces. We prove that M-FYS is isomorphic to ILM-FTOP—the category of induced LM-fuzzy topological spaces—and ILM-FTOP is a reflective and coreflective full subcategory of SLM-FTOP. Finally, we study weakly induced modification of LM-fuzzy topologies and show that WILM-FTOP—the category of weakly induced LM-fuzzy topological spaces—is a reflective and coreflective full subcategory of LM-FTOP.