(IC)LM-FUZZY TOPOLOGICAL SPACES

The aim of the present paper is to define and study (IC)$LM$-fuzzy topological spaces, a generalization of (weakly) induced $LM$-fuzzy topological spaces. We discuss the basic properties of (IC)$LM$-fuzzy topological spaces, and introduce the notions of interior (IC)-fication and exterior (IC)-fication of $LM$-fuzzy topologies and prove that {bf ICLM-FTop} (the category of (IC)$LM$-fuzzy topological spaces) is an isomorphism-closed full proper subcategory of {bf LM-FTop} (the category of $LM$-fuzzy topological spaces) and {bf ICLM-FTop} is a simultaneously bireflective and bicoreflective full subcategory of {bf LM-FTop}.