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Some Results on Soft Topological Notions

Year 2021, Volume: 10 Issue: 1, 65 - 75, 30.04.2021

Tuğçe Aydın Serdar Enginoğlu

Abstract

Recently, the generalizations of soft open sets have become a popular subject. These generalizations define based on the concepts of the soft interior and soft closure. Therefore, the properties related to these concepts play an essential role in propositions concerning the generalizations. To this end, we consider the soft interior and soft closure through the concept of the soft element, and thus we clarify the relationships between a soft topological space and its soft subspace topologies. Afterwards, we mention soft α-open sets, soft α-closed sets, and soft α-T_0 space via soft elements. Finally, we discuss soft α-separation axioms for further research.

Keywords

Soft sets Soft open sets Soft topology Soft α-open sets Soft α-T_0 space

References

  • D, Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4–5), (1999) 19–31.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Computers and Mathematics with Applications, 62(1), (2011) 351–358.
  • M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61, (2011) 1786–1799.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On soft topology, El-Cezerî Journal of Science and Engineering, 2(3), (2015) 23–38.
  • S. K. Nazmul, S. K. Samanta, Neighbourhood properties of soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 6(1), (2013) 1–15.
  • S. Hussain, B. Ahmad, Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3), (2015) 559–568.
  • G. Şenel, N. Çağman, Soft topological subspaces, Annals of Fuzzy Mathematics and Informatics, 10(4), (2015) 525–535.
  • T. Aydın, On soft topology, Master’s Thesis, Çanakkale Onsekiz Mart University (2016) Çanakkale, Turkey (in Turkish).
  • J. Thomas, S. J. John, A note on soft topology, Journal of New Results in Science, 11, (2016) 24–29.
  • M. Matejdes, Some remarks on soft separation axioms, International Journal of Pure and Applied Mathematics, 116(1), (2017) 191–195.
  • T. Y. Öztürk, S. Bayramov, Topology on soft continuous function spaces, Mathematical and Computational Applications, 22(2), (2017) 1–11.
  • S. Goldar, S. Ray, A study of soft topological axioms and soft compactness by using soft elements, Journal of New Results in Science, 8(2), (2019) 53–66.
  • M. Kiruthika, P. Thangavelu, A link between topology and soft topology, Hacettepe Journal of Mathematics and Statistics, 48(3), (2019) 800–804.
  • K. Taşköprü, I. Altıntaş, A new approach for soft topology and soft function via soft element, Mathematical Methods in the Applied Sciences, (2020) 1–15. https://doi.org/10.1002/mma.6354
  • M. Akdağ, A. Özkan, Soft α-open sets and soft α-continuous functions, Abstract and Applied Analysis, 2014, (2014) Article ID 891341, 1–7.
  • I. Arockiarani, A. A. Lancy, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces, International Journal of Mathematical Archive, 4(2), (2013) 1–7.
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics and Information Sciences, 7(1), (2013) 287–294.
  • M. Akdağ, A. Özkan, On soft α-separation axioms, Journal of Advanced Studies in Topology 5(4), (2014b) 16–24.
  • A. M. Khattak, G. A. Khan, M. Ishfaq, F. Jamal, Characterization of soft α-separation axioms and soft β-separation axioms in soft single point spaces and in soft ordinary spaces, Journal of New Theory, (19), (2017) 63–81.
  • S. Saleh, K. Hur, On some lower soft separation axioms, Annals of Fuzzy Mathematics and Informatics, 19(1), (2020) 61–72.
  • N. Çağman, S. Enginoğlu, Soft sets theory and uni-int decision-making, European Journal of Operational Research, 207(2), (2010) 848–855.
  • İ. Zorlutuna, M. Akdağ, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2), (2012) 171–185.
  • A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-Latif, γ-operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 7(2), (2014) 181–196.

Year 2021, Volume: 10 Issue: 1, 65 - 75, 30.04.2021

Tuğçe Aydın Serdar Enginoğlu

Abstract

References

  • D, Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4–5), (1999) 19–31.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Computers and Mathematics with Applications, 62(1), (2011) 351–358.
  • M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61, (2011) 1786–1799.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On soft topology, El-Cezerî Journal of Science and Engineering, 2(3), (2015) 23–38.
  • S. K. Nazmul, S. K. Samanta, Neighbourhood properties of soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 6(1), (2013) 1–15.
  • S. Hussain, B. Ahmad, Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3), (2015) 559–568.
  • G. Şenel, N. Çağman, Soft topological subspaces, Annals of Fuzzy Mathematics and Informatics, 10(4), (2015) 525–535.
  • T. Aydın, On soft topology, Master’s Thesis, Çanakkale Onsekiz Mart University (2016) Çanakkale, Turkey (in Turkish).
  • J. Thomas, S. J. John, A note on soft topology, Journal of New Results in Science, 11, (2016) 24–29.
  • M. Matejdes, Some remarks on soft separation axioms, International Journal of Pure and Applied Mathematics, 116(1), (2017) 191–195.
  • T. Y. Öztürk, S. Bayramov, Topology on soft continuous function spaces, Mathematical and Computational Applications, 22(2), (2017) 1–11.
  • S. Goldar, S. Ray, A study of soft topological axioms and soft compactness by using soft elements, Journal of New Results in Science, 8(2), (2019) 53–66.
  • M. Kiruthika, P. Thangavelu, A link between topology and soft topology, Hacettepe Journal of Mathematics and Statistics, 48(3), (2019) 800–804.
  • K. Taşköprü, I. Altıntaş, A new approach for soft topology and soft function via soft element, Mathematical Methods in the Applied Sciences, (2020) 1–15. https://doi.org/10.1002/mma.6354
  • M. Akdağ, A. Özkan, Soft α-open sets and soft α-continuous functions, Abstract and Applied Analysis, 2014, (2014) Article ID 891341, 1–7.
  • I. Arockiarani, A. A. Lancy, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces, International Journal of Mathematical Archive, 4(2), (2013) 1–7.
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics and Information Sciences, 7(1), (2013) 287–294.
  • M. Akdağ, A. Özkan, On soft α-separation axioms, Journal of Advanced Studies in Topology 5(4), (2014b) 16–24.
  • A. M. Khattak, G. A. Khan, M. Ishfaq, F. Jamal, Characterization of soft α-separation axioms and soft β-separation axioms in soft single point spaces and in soft ordinary spaces, Journal of New Theory, (19), (2017) 63–81.
  • S. Saleh, K. Hur, On some lower soft separation axioms, Annals of Fuzzy Mathematics and Informatics, 19(1), (2020) 61–72.
  • N. Çağman, S. Enginoğlu, Soft sets theory and uni-int decision-making, European Journal of Operational Research, 207(2), (2010) 848–855.
  • İ. Zorlutuna, M. Akdağ, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2), (2012) 171–185.
  • A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-Latif, γ-operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 7(2), (2014) 181–196.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Tuğçe Aydın 0000-0002-8134-1004

Serdar Enginoğlu 0000-0002-7188-9893

Publication Date April 30, 2021
Published in Issue Year 2021 Volume: 10 Issue: 1

Cite

APA Aydın, T., & Enginoğlu, S. (2021). Some Results on Soft Topological Notions. Journal of New Results in Science, 10(1), 65-75.
AMA Aydın T, Enginoğlu S. Some Results on Soft Topological Notions. JNRS. April 2021;10(1):65-75.
Chicago Aydın, Tuğçe, and Serdar Enginoğlu. “Some Results on Soft Topological Notions”. Journal of New Results in Science 10, no. 1 (April 2021): 65-75.
EndNote Aydın T, Enginoğlu S (April 1, 2021) Some Results on Soft Topological Notions. Journal of New Results in Science 10 1 65–75.
IEEE T. Aydın and S. Enginoğlu, “Some Results on Soft Topological Notions”, JNRS, vol. 10, no. 1, pp. 65–75, 2021.
ISNAD Aydın, Tuğçe - Enginoğlu, Serdar. “Some Results on Soft Topological Notions”. Journal of New Results in Science 10/1 (April 2021), 65-75.
JAMA Aydın T, Enginoğlu S. Some Results on Soft Topological Notions. JNRS. 2021;10:65–75.
MLA Aydın, Tuğçe and Serdar Enginoğlu. “Some Results on Soft Topological Notions”. Journal of New Results in Science, vol. 10, no. 1, 2021, pp. 65-75.
Vancouver Aydın T, Enginoğlu S. Some Results on Soft Topological Notions. JNRS. 2021;10(1):65-7.
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