Covering dimension and normality in L-topological spaces

Abstract

Purpose: In this paper, we extend the concept of covering dimension of general topological spaces to L-topological spaces using α-Q-covers and quasi-coincidence relation. Methods: Dimension theory is a branch of topology devoted to the definition and study of the notion of dimension in certain classes of topological spaces. The dimension of a general topological space X can be defined in three different ways: the small inductive dimension indX, the large inductive dimension IndX, and the covering dimension dimX. The covering dimension dim behaves somewhat better than the other two dimensions, i.e., that for the dimension dim, a large number of theorems of the classical theory can be extended to general topological spaces. Also, there is a substantial theory of covering dimension for normal spaces. Results: A characterization of covering dimension in the weakly induced L-topological spaces is obtained. Moreover, a characterization of covering dimension for fuzzy normal spaces is also obtained. Conclusions: Finally, This paper provides some brief sketches regarding the topics covering dimension in L-topological spaces and covering dimension for fuzzy normal spaces. The neighborhood structure used for the investigations is the quasi-coincident neighborhood structure.