(IC)LM-FUZZY TOPOLOGICAL SPACES

Abstract

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