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.

The main purpose of this paper is to introduce a some concepts in fibrewise totally topological space which are called fibrewise totally mapping, fiberwise totally closed mapping, fibrewise weakly totally closed mapping, fibrewise totlally perfect mapping fibrewise almost totally perfect mapping. Also the concepts as totally adherent point, filter, filter base, totally converges to a subset, totally directed toward a set, totally rigid, totally-H-set, totally Urysohn space, locally totally-QHC totally topological space are introduced and the main concept in this paper is fibrewise totally perfect mapping in totally top

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result. 

The objective of this work is to study the concept of a fuzzy -cone metric space And some related definitions in space. Also, we discuss some new results of fixed point theorems. Finally, we apply the theory of fixed point achieved in the research on an integral type.

Soft closure spaces are a new structure that was introduced very recently. These new spaces are based on the notion of soft closure operators. This work aims to provide applications of soft closure operators. We introduce the concept of soft continuous mappings and soft closed (resp. open) mappings, support them with examples, and investigate some of their properties.

In this thesis, we introduced the simply* compact spaces which are defined over simply* open set, and study relation between the simply* separation axioms and the compactness were studied and study a new types of functions known as αS^(M* )- irresolte , αS^(M* )- continuous and R S^(M* )- continuous, which are defined between two topological spaces. On the other hand we use the class of soft simply open set to define a new types of separation axioms in soft topological spaces and we introduce the concept of soft simply compactness and study it. We explain and discuss some new concepts in soft topological spaces such as soft simply separated, soft simply disjoint, soft simply division, soft simply limit point and we define soft simply c

The primary objective of this paper is to introduce a new concept of fibrewise topological spaces on D is named fibrewise multi- topological spaces on D. Also, we entroduce the concepts of multi-proper, fibrewise multi-compact, fibrewise locally multi-compact spaces, Moreover, we study relationships between fibrewise multi-compact (resp., locally multi-compac) space and some fibrewise multi-separation axioms.