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Some Spaces in Neutrosophic e-Open Sets

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Algebra, Analysis, and Associated Topics

Abstract

In neutrosophic topological space, the notion of neutrosophic e connectedness and disconnectedness is introduced in this chapter. In addition, we also introduced neutrosophic e separated sets, and finally, we analyze neutrosophic e compact spaces and related features in neutrosophic topological spaces.

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References

  1. Acikgoza, A., Esenbel, F.: A Study on Connectedness in Neutrosophic Topological Spaces. AIP Conference Proceedings. 2334, 020003 (2021).

    Article  Google Scholar 

  2. Arar, M.: About Neutrosophic Countably Comapctness. Neutrosophic Sets and Systems. 36, 246–255 (2020).

    Google Scholar 

  3. Arokiarani, I., Dhavaseelan, R., Jafari, S., Parimala, M.: On some new notions and functions in neutrosophic topological spaces. Neutrosophic Sets and Systems, 16, 16–19 (2017).

    Google Scholar 

  4. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 87–96 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  5. Chandrasekar, V., Sobana, D., Vadivel, A.: On Fuzzy e-open Sets, Fuzzy e-continuity and Fuzzy e-compactness in Intuitionistic Fuzzy Topological Spaces. Sahand Communications in Mathematical Analysis (SCMA). 12 (1), 131–153 (2018).

    Google Scholar 

  6. Chang, C.L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24, 182–190 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  7. Coker, D.: An introduction to intuitionistic fuzzy topological spaces. Fuzzy sets and systems. 88, 81–89 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  8. Ekici, E.: On e-open sets, \( \mathcal {D}\mathcal {P}^{\star }\)-sets and \(\mathcal {D}\mathcal {P} \epsilon ^{\star }\)-sets and decomposition of continuity. The Arabian Journal for Science and Engineering. 33 (2A), 269–282 (2008).

    Google Scholar 

  9. Ekici, E.: Some generalizations of almost contra-super-continuity. Filomat. 21 (2), 31–44 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  10. Ekici, E.: New forms of contra-continuity. Carpathian Journal of Mathematics. 24 (1), 37–45 (2008c).

    MathSciNet  MATH  Google Scholar 

  11. Ekici, E.: On e-open sets and (D, S)-sets. Mathematica Moravica. 13 (1), 29–36 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  12. Ekici, E.: On a-open sets, A-sets and decompositions of continuity and super-continuity. Annales Univ. Sci. Budapest. EÃűtvÃűs Sect. Math. 51, 39–51 (2008).

    Google Scholar 

  13. Ekici, E.: A note on a-open sets and e-open sets. Filomat. 22 (1), 89–96 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  14. Parimala, M., Karthika, M., Jafari, S., Smarandache, F., El-Atik, A.A.: Neutrosophic αψ-connectedness. Journal of Intelligent & Fuzzy Systems. 38, 853–857 (2020).

    Google Scholar 

  15. Saha, S.: Fuzzy δ-continuous mappings. Journal of Mathematical Analysis and Applications. 126, 130–142 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  16. Salama, A.A., Alblowi, S.A.: Neutrosophic set and neutrosophic topological spaces. IOSR Journal of Mathematics. 3 (4), 31–35 (2012).

    Article  Google Scholar 

  17. Salama, A.A., Smarandache, F.: Neutrosophic crisp set theory. USA: Educational Publisher (2015).

    Google Scholar 

  18. Seenivasan, V., Kamala, K.: Fuzzy e-continuity and fuzzy e-open sets. Annals of Fuzzy Mathematics and Informatics. 8, 141–148 (2014).

    MathSciNet  MATH  Google Scholar 

  19. Smarandache, F.: A Unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability. Rehoboth: American Research Press (1999).

    MATH  Google Scholar 

  20. Smarandache, F.: Neutrosophy and neutrosophic logic. 1st Int. Conf. on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics. University of New Mexico, Gallup, NM, 87301 USA (2002).

    Google Scholar 

  21. Vadivel, A., Mohanarao Nauvluri, Thangaraja, P.: On Nnc DP*-sets and decomposition of continuity in Nnc-topological spaces. Adv. Math: Sci. J. 9 (11), 9559–9564 (2020).

    Google Scholar 

  22. Vadivel, A., Mohanarao Nauvluri, Thangaraja, P.: Characterization of completely Nnc (weakly Nnc)-irresolute functions via Nnce-open sets. J. Phys. Conf. Ser. 1724, 012009 (2021).

    Google Scholar 

  23. Vadivel, A., Mohanarao Nauvluri, Thangaraja, P.: Completely Nnce(weakly Nnce)-irresolute functions via Nnce-open sets. J. Phys. Conf. Ser. 1724, 012010 (2021).

    Google Scholar 

  24. Vadivel, A., Seenivasan, M., John Sundar, C.: An introduction to δ-open sets in a neutrosophic topological spaces. Journal of Physics: Conference Series. 1724, 012011 (2021).

    Google Scholar 

  25. Vadivel, A., John Sundar, C.: Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science (IJNS). 13 (2), 66–74 (2021).

    Google Scholar 

  26. Vadivel, A., John Sundar, C.: New Operators Using Neutrosophic δ-Open Set. Journal of Neutrosophic and Fuzzy Systems. 1 (2), 61–70 (2021).

    Article  Google Scholar 

  27. Vadivel, A., Thangaraja, P., John Sundar, C.: Neutrosophic e-continuous maps and neutrosophic e-irresolute maps. Turkish Journal of Computer and Mathematics Education. 12 (1S), 369–375 (2021).

    Google Scholar 

  28. Vadivel, A., Thangaraja, P., John Sundar, C.: Neutrosophic e-Open Maps, Neutrosophic e-Closed Maps and Neutrosophic e-Homeomorphisms in Neutrosophic Topological Spaces. AIP Conference Proceedings. 2364, 020016 (2021).

    Article  Google Scholar 

  29. Vadivel, A., Thangaraja, P.: e-open sets in Nnc-topological spaces. J. Phys. Conf. Ser. 1724, 012007 (2021).

    Google Scholar 

  30. Vadivel, A., Thangaraja, P.: e-continuous and somewhat e-continuity in Nnc-topological spaces. J. Phys. Conf. Ser. 1724, 012008 (2021).

    Google Scholar 

  31. Zadeh, L.A.: Fuzzy sets. Information and control. 8, 338–353 (1965).

    Article  MathSciNet  MATH  Google Scholar 

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The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of the paper.

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Vadivel, A., Thangaraja, P., John Sundar, C. (2022). Some Spaces in Neutrosophic e-Open Sets. In: Singh, S., Sarigöl, M.A., Munjal, A. (eds) Algebra, Analysis, and Associated Topics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-19082-7_14

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