In this research, we introduce and study the concept of fibrewise bitopological spaces. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces,(resp., open, locally sliceable and locally sectionable). We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise T_0 spaces, fibrewise pairwise T_1 spaces, fibrewise pairwise R_0 spaces, fibrewise pairwise Hausdorff spaces, fibrewise pairwise functionally Hausdorff spaces, fibrewise pairwise regular spaces, fibrewise pairwise completely regular spaces, fibrewise pairwise normal spaces, and fibrewise pairwise functionally normal spaces. In addition, we offer some results concerning these extended axioms. Finally, we introduce some concepts in fibrewise bitopological spaces which are fibrewise ij-bitopological spaces, fibrewise ij-closed bitopological spaces, fibrewise ij-compact bitopological spaces, fibrewise ij-perfect bitopological spaces, fibrewise weakly ij-closed bitopological space, fibrewise almost ij-perfect bitopological space, fibrewise ij^*-bitopological spaces. We study several theorems and characterizations concerning these concepts.
<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>
the electron correlation effect for inter-shell can be described by evaluating the fermi hole and partial fermi hole for Li atom comparing with Be+ and B+2 ions
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.
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Sequences spaces , m , p have called quasi-Sobolev spaces were introduced by Jawad . K. Al-Delfi in 2013 [1]. In this paper , we deal with notion of quasi-inner product space by using concept of quasi-normed space which is generalized to normed space and given a relationship between pre-Hilbert space and a quasi-inner product space with important results and examples. Completeness properties in quasi-inner product space gives us concept of quasi-Hilbert space . We show that , not all quasi-Sobolev spa
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In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.
Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity
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.
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Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.