Generalizations of Lindelof Properties in Bitopological Spaces : Generalized Lindelöf, Mappings, Semiregular and Product Properties

We are concerned with the ideas of pairwise Lindelf, generalizations of pairwise Lindelf and pairwise regular-Lindelf in bitopological space. There are four kinds of pairwise Lindelf, i.e., Lindelf, B-Lindelf, s-Lindelf and p-Lindelf and three kinds of generalized pairwise Lindelf, i.e., pairwise nearly Lindelf, pairwise almost Lindelf and pairwise weakly Lindelf. Another idea is leads to the pairwise nearly regular-Lindelf, pairwise almost regular-Lindelf and pairwise weakly regular-Lindelf. Some characterizations of these new spaces are given. The relations among them are studied. Subspaces are also studied and some of their characterizations investigated. We show that some subsets inherit these generalized pairwise covering properties. Mappings and generalized pairwise continuities are also studied. The effect of mappings on these generalized properties is investigated. We show that some mappings preserve these pairwise covering properties. It is shown that some of the generalized properties are pairwise semiregular properties. The productivity of these generalized properties are studied. We show that the pairwise Lindelf are not preserved under finite products.