International Journal of Neutrosophic Science (IJNS) Vol. 16, No. 2, PP. 62-71, 2021 DOI: https://doi.org/10.54216/IJNS.160201 Received: June 21, 2021 Accepted: November 10, 2021 62 Continuity and Compactness on Neutrosophic Soft Bitopological Spaces Ahmed B. AL-Nafee 1* , Jamal K. Obeed 2 , Huda E. Khalid 3 1* Ministry of Education Open Educational College, Department of Mathematics, Babylon, Iraq. " Ahm_math_88@yahoo.com" 2 University Of Missan, College Of Basic Education, Department Of Mathematics, Iraq. jamal.k@uokerbala.edu.iq 3 Telafer University, Scientific Affairs and Cultural Relations Dept., Telafer, Iraq. dr.huda-ismael@uotelafer.edu.iq. " *Correspondence: Ahm_math_88@yahoo.com " Abstract: In this manuscript, continuity, compactness concepts in neutrosophic soft bitopologi-cal space have been defined using star bineutrosophic soft open notion. Theorems and properties concerning to these two notions have been investigated here. Keyword: Neutrosophic Soft Set, Fuzzy Set, Star Bineutrosophic Soft Open, Neutrosophic Soft Bitopological Spaces. 1. Introduction The notion of soft set as a general mathematical tool for coping with objects involving vagueness and uncertainty has been introduced by Molodtsov [2]. F. Smarandache [3] introduced the concept of neutrosophic sets which is a generalization of Zadeh’s .. fuzzy set, and Atanassov's .. intuitionistic fuzzy set, as a new mathematical tool for dealing with problems involving indeterminacy, inconsistent knowledge, incompleteness. In 2013, the notion of neutrosophic soft set was introduced by merging soft set concept and neutrosophic set concept, and later this concept and its operations have been redefined (see, [5,6,7]). The notion of neutrosophic soft topological spaces was presented by [8], and later this concept has been redefined by [9] differently from the study [8]. In 2021, Al-Nafee, et al. [1] generalized the concept of neutrosophic soft topological spaces to the concept of neutrosophic soft bitopological spaces and they investigated several related properties and theories. The concepts of neutrosophic soft continuous mapping and compactness with their properties and some theorems were presented by many authors (see [8,10,11,12]). For more details on these concepts, you can see [13-20]. In this manuscript, the authors introduced the concepts of continuity, compactness and Hausdorff in neutrosophic soft bitopological spaces, through presenting the concepts of N3(bi) * -continuous mapping, NSbi-open mapping, NSbi-closed mapping, N3(bi) * -compact and N3(bi) * -Hausdorff based on the definition of N3(bi) * -open, some of related theorems and properties also have investigated. 2. . Basic Concepts In this section, some basic and related definitions are recalled as background and to give the reader a deep insight on the basic tools of the upcoming section. For the purpose of abbreviation, the authors will denote to the neutrosophic soft set by (NSS). Also the soft set is denoted by (SS). Definition 2.1 [3] The neutrosophic'set S over G is defined.as follows: S = {< g‚ I S (g)‚ B S (g)‚ F S (g) >) ∶ g ∈ G }, where the functions, I,B,F : G →] − 0,+1[ and - 0 ≤ I S (g) + B S (g) + F S (g) ≤ +3. "(( From philosophical point of view the neutrosophic set takes the value from real standard or non- standard subsets of ]−0.,+1[ . But in real life application in scientific and engineering problems it is difficult to use a neutrosophic set with value from real standard or non-standard subset of ]−0.,+1[. Hence we consider the neutrosophic set which takes the value from the subset of [0, 1]))".