lg-paracompactness of lg-fuzzy topological metric spaces

In this manuscript, we introduce lgc -fuzzy euclidean topological space in which l denotes a completely distributive lattice with a countable subset dense in it. we use the structure of lg-fuzzy topological space (x, t), which x is an l-fuzzy subset of the crisp set m and t : lm x → l, is an l-gradation of openness on x to define the fundamental concepts of lg-fuzzy analysis such as lg-locally compactness and lg-paracompactness and prove several theorems. in consequence, we show that any second countable hausdorff lg-fuzzy topological space that is lg-locally compact is lg-paracompact. also from any given metric ρ on a crisp set m and l-fuzzy subset x of it, we construct an lgradation of openness tρ on x and obtain lg-fuzzy topological metric space (x, tρ). finally, we prove an interesting theorem: every lg-fuzzy topological metric space, is lg-paracompact.