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Keywords = r-single-valued neutrosophic separated

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18 pages, 322 KiB  
Article
£-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces
by Fahad Alsharari
Symmetry 2021, 13(1), 53; https://doi.org/10.3390/sym13010053 - 31 Dec 2020
Cited by 3 | Viewed by 2091
Abstract
This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, [...] Read more.
This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied. Full article
20 pages, 811 KiB  
Article
Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces
by Yaser Saber, Fahad Alsharari, Florentin Smarandache and Mohammed Abdel-Sattar
Symmetry 2020, 12(9), 1464; https://doi.org/10.3390/sym12091464 - 7 Sep 2020
Cited by 18 | Viewed by 2482
Abstract
This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it [...] Read more.
This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations. Full article
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