A topological view on L-fuzzy soft sets: Degree of countably compactness and the Lindelöf property

Keywords: Fuzzy soft set, fuzzy soft topology, compactness, countably compactness, Lindelof property. 1 Introduction The soft set theory, initiated by Molodtsov [24] in 1999, is one of the mathematical methods that aims to describe phenomena and concepts of ambiguous, undefined and imprecise meaning. Later in her seminal papers Cetkin [14,15] have presented the parameterized degree of semi-precompactness and the compactness in the fuzzy soft universe. The definitions of countable compactness and the Lindelof property in L-topological spaces have been introduced by Shi [31]. Besides we refer [4,5,6,16,17] for the compactness in the soft unverse. In conclude, we investigate the relations among parameterized compactness degree, countably compactness degree and the degree of having the Lindelof property. 2 Preliminaries Throughout this paper, X refers to a nonempty initial universe, E,K denotes the arbitrary nonempty sets viewed on the sets of parameters and L = (L, V, A/) denotes a complete DeMorgan algebra with the smallest element Ol and the largest element \l- With the underlying lattice L, a mapping A :