Lowen LM-fuzzy topological spaces

The aim of this paper is to define and study Lowen LM-fuzzy topological spaces. We discuss the basic properties of Lowen LM-fuzzy topological spaces, and introduce the notions of interior Lowen topology and exterior Lowen topology of an LM-fuzzy topology and prove that LLM-FTop (the category of Lowen LM-fuzzy topological spaces) is isomorphism-closed and simultaneously bireflective and bicoreflective in SLM-FTop (the category of stratified LM-fuzzy topological spaces). Moreover, we also prove that an LM-fuzzy topological space is an induced LM-fuzzy topological space iff it is a Lowen LM-fuzzy topological space and an (IC)LM-fuzzy topological space.

► The definition of Lowen LM-fuzzy topological spaces is introduced.
► The interior Lowen topology and exterior Lowen topology of an LM-fuzzy topology are introduced.
► Some basic properties and categorical properties of Lowen LM-fuzzy topological spaces are studied.
► It is proved that LLM-FTop is simultaneously bireflective and bicoreflective in SLM-FTop.