In this thesis, we introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essential separation axioms of ordinary soft topology namely fibrewise soft near T_0 spaces, fibrewise soft near T_1 spaces, fibrewise soft near R_0 spaces, fibrewise soft near Hausdorff spaces, fibrewise soft near functionally Hausdorff spaces, fibrewise soft near regular spaces, fibrewise soft near completely regular spaces, fibrewise soft near normal spaces and fibrewise soft near functionally normal spaces. Too we add numerous outcomes about it. Finally, we introduced a notion fibrewise soft ideal topological spaces and give the results related it to, Further we obtain some properties in the light of the study notions fibrewise soft ideal open topological spaces, fibrewise soft ideal closed topological spaces and fibrewise soft near ideal topological spaces.
In this paper, we introduce a new class of sets, namely , s*g-ï¡-open sets and we show that the family of all s*g-ï¡-open subsets of a topological space ) ,X( ï´ from a topology on X which is finer than ï´ . Also , we study the characterizations and basic properties of s*g-ï¡open sets and s*g-ï¡-closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g- ï¡ -continuous functions and s*g- ï¡ -irresolute functions in topological spaces . Some properties of these functions have been studied .
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In this paper we introduce a new type of functions called the generalized regular
continuous functions .These functions are weaker than regular continuous functions and
stronger than regular generalized continuous functions. Also, we study some
characterizations and basic properties of generalized regular continuous functions .Moreover
we study another types of generalized regular continuous functions and study the relation
among them
In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.
The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate
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The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.
The aim of this paper is to introduce the concept of N and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.
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This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor
... Show MoreThe soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.
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