In this thesis, we introduced some kinds of fibrewise topological spaces by using totally continuous function is called fibrewise totally topological spaces. We generalize some fundamental results from fibrewise topology into fibrewise totally topological spaces. We also introduce the concepts of fibrewise totally separation axioms, fibrewise totally compact and locally totally compact topological spaces. As well as fibrewise totally perfect topological spaces. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise totally topological spaces. We, also introduce the concepts of fibrewise totally closed topological spaces, fibrewise totally open topological spaces, fibrewise locally sliceable and locally sectionable totally topological spaces. One the other hand, we studied fibrewise totally forms of the more essential separation axioms of ordinary topology namely fibrewise totally T_0 spaces, fibrewise totally T_1 spaces, fibrewise totally R_0 spaces, fibrewise totally Hausdorff spaces, fibrewise totally functionally Hausdorff spaces, fibrewise totally regular spaces, fibrewise totally completely regular spaces, fibrewise totally normal spaces and fibrewise totally functionally normal spaces. Too we add numerous outcomes about it. As well as, we introduced a notion fibrewise totally compact and fibrewise locally totally compact topological spaces. Finally, we introduced a notion fibrewise totally perfect topological spaces, fibrewise weakly totally closed topological spaces, fibrewise totally rigidlly sets, fibrewise totally almost perfect topological spaces and fibrewise T^*topological spaces. We study several theorm and characterizations converning these concepts.
The concept of -closedness, a kind of covering property for topological spaces, has already been studied with meticulous care from different angles and via different approaches. In this paper, we continue the said investigation in terms of a different concept viz. grills. The deliberations in the article include certain characterizations and a few necessary conditions for the -closedness of a space, the latter conditions are also shown to be equivalent to -closedness in a - almost regular space. All these and the associated discussions and results are done with grills as the prime supporting tool.
This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.
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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 introduce and study the concept of a new class of generalized closed set which is called generalized b*-closed set in topological spaces ( briefly .g b*-closed) we study also. some of its basic properties and investigate the relations between the associated topology.
The objective of this paper is to define and introduce a new type of nano semi-open set which called nano -open set as a strong form of nano semi-open set which is related to nano closed sets in nano topological spaces. In this paper, we find all forms of the family of nano -open sets in term of upper and lower approximations of sets and we can easily find nano -open sets and they are a gate to more study. Several types of nano open sets are known, so we study relationship between the nano -open sets with the other known types of nano open sets in nano topological spaces. The Operators such as nano -interior and nano -closure are the part of this paper.
The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.
This paper introduces cutpoints and separations in -connected topological spaces, which are constructed by using the union of vertices set and edges set for a connected graph, and studies the relationships between them. Furthermore, it generalizes some new concepts.
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The concept of separation axioms constitutes a key role in general topology and all generalized forms of topologies. The present authors continued the study of gpα-closed sets by utilizing this concept, new separation axioms, namely gpα-regular and gpα-normal spaces are studied and established their characterizations. Also, new spaces namely gpα-Tk for k = 0, 1, 2 are studied.
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 .
In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Æ„c-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Æ„ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.
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