In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.

The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.

In this article, the notions  are introduced by using soft ideal and soft semi-open sets, which are - - - -closed sets " -closed" where many of the properties of these sets are clarified. Some games by using soft- -semi, soft separation axioms: like ( ₀   ( ₀  Using many figures and proposition to study the relationships among these kinds of games with some examples are explained.