Research Article
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NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES

Year 2023, , 89 - 98, 31.01.2023

Zehra Güzel Ergül

https://doi.org/10.33773/jum.1202907

Abstract

The aim of this paper is to produce new decompositions of soft continuity.
For this reason, we first have introduced two new sets concepts named as
soft AC-set with soft BC-set in soft topological spaces. Compairing with
this two soft sets concepts and others soft set kinds, we have obtained two
decompositions of soft open sets, supported by counterexamples. Utilizing
soft AC-set and soft BC-set concepts, we have introduced two functions
concepts named as soft AC-continuous with soft BC-continuous functions and
we have obtained a new decomposition of soft continuity.

Keywords

Soft set Soft topological space Soft AC-set Soft BC-set Soft AC-continuity Soft BC-continuity.

References

  • M. Akdağ and A. Özkan, Soft _-open sets and soft _-continuous functions, Abstract and Applied Analysis, http://dx.doi.org/10.1155/2014/891341 (2014).
  • M. Akdağ and A. Özkan, Soft b-open sets and soft b-continuous functions, Math. Sci. 8(124), pp. 1-9 (2014).
  • A. Aygünoğlu and H. Aygün, Some notes on soft topological spaces, Neural Computing and Applications, 21(1) pp. 113-119 (2012).
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics & Information Sciences 7(1), pp. 287-294 (2013).
  • F. Feng, Y. B. Jun and X. Z. Zhao, Soft semirings, Computers and Mathematics with Applications 56, pp. 2621-2628 (2008).
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Computers and Mathematics with Applications 62(11), pp. 4058-4067 (2011).
  • A. Kharal and B. Ahmad, Mappings on soft classes, New Mathematics and Natural Computation 7(3), pp. 471-481 (2011).
  • J. Mahanta and P. K. Das, On soft topological space via semi-open and semiclosed soft sets, Cornell University Library arXiv:1203.4133 (2012).
  • P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45(4-5), pp. 555-562 (2003).
  • W. K. Min, A note on soft topological spaces, Computers and Mathematics with Applications 62(9), pp. 3524-3528 (2011).
  • D. Molodtsov, Soft set theory-_rst results, Computers and Mathematics with Applications 37(4-5), pp. 19-31 (1999).
  • M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications 61(7), pp. 1786-1799 (2011).
  • N. Tozlu, Ş. Yüksel and Z. Güzel Ergül, Soft C-Sets and a Decomposition of Soft Continuity in Soft Topological Spaces, International Journal of Mathematics Trends and Technology 16(1), pp. 58-69 (2014).
  • N. Tozlu and Ş. Yüksel, Soft A-sets and soft B-sets in soft topological spaces, Mathematical Sciences and Applications E-Notes 5(2), pp. 17-25 (2017). Z. Güzel Ergül and N. Tozlu, Decompositions of soft continuity and soft AB-continuity, Annals of Fuzzy Mathematics and Informatics 14(5), pp. 463-474 (2017).
  • Ş. Yüksel, N. Tozlu and Z. Güzel Ergül, Soft regular generalized closed sets in soft topological spaces, International Journal of Mathematical Analysis 8(8), pp. 355-367 (2014).
  • I. Zorlutuna, M. Akda_g, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3(2), pp. 171-185 (2012).

Year 2023, , 89 - 98, 31.01.2023

Zehra Güzel Ergül

https://doi.org/10.33773/jum.1202907

Abstract

Keywords

Soft set Soft topological space Soft AC-set Soft BC-set Soft AC-continuity Soft BC-continuity.

References

  • M. Akdağ and A. Özkan, Soft _-open sets and soft _-continuous functions, Abstract and Applied Analysis, http://dx.doi.org/10.1155/2014/891341 (2014).
  • M. Akdağ and A. Özkan, Soft b-open sets and soft b-continuous functions, Math. Sci. 8(124), pp. 1-9 (2014).
  • A. Aygünoğlu and H. Aygün, Some notes on soft topological spaces, Neural Computing and Applications, 21(1) pp. 113-119 (2012).
  • B. Chen, Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics & Information Sciences 7(1), pp. 287-294 (2013).
  • F. Feng, Y. B. Jun and X. Z. Zhao, Soft semirings, Computers and Mathematics with Applications 56, pp. 2621-2628 (2008).
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Computers and Mathematics with Applications 62(11), pp. 4058-4067 (2011).
  • A. Kharal and B. Ahmad, Mappings on soft classes, New Mathematics and Natural Computation 7(3), pp. 471-481 (2011).
  • J. Mahanta and P. K. Das, On soft topological space via semi-open and semiclosed soft sets, Cornell University Library arXiv:1203.4133 (2012).
  • P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45(4-5), pp. 555-562 (2003).
  • W. K. Min, A note on soft topological spaces, Computers and Mathematics with Applications 62(9), pp. 3524-3528 (2011).
  • D. Molodtsov, Soft set theory-_rst results, Computers and Mathematics with Applications 37(4-5), pp. 19-31 (1999).
  • M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications 61(7), pp. 1786-1799 (2011).
  • N. Tozlu, Ş. Yüksel and Z. Güzel Ergül, Soft C-Sets and a Decomposition of Soft Continuity in Soft Topological Spaces, International Journal of Mathematics Trends and Technology 16(1), pp. 58-69 (2014).
  • N. Tozlu and Ş. Yüksel, Soft A-sets and soft B-sets in soft topological spaces, Mathematical Sciences and Applications E-Notes 5(2), pp. 17-25 (2017). Z. Güzel Ergül and N. Tozlu, Decompositions of soft continuity and soft AB-continuity, Annals of Fuzzy Mathematics and Informatics 14(5), pp. 463-474 (2017).
  • Ş. Yüksel, N. Tozlu and Z. Güzel Ergül, Soft regular generalized closed sets in soft topological spaces, International Journal of Mathematical Analysis 8(8), pp. 355-367 (2014).
  • I. Zorlutuna, M. Akda_g, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3(2), pp. 171-185 (2012).
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Zehra Güzel Ergül 0000-0001-5717-1626

Publication Date January 31, 2023
Submission Date November 11, 2022
Acceptance Date January 30, 2023
Published in Issue Year 2023

Cite

APA Güzel Ergül, Z. (2023). NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES. Journal of Universal Mathematics, 6(1), 89-98. https://doi.org/10.33773/jum.1202907
AMA Güzel Ergül Z. NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES. JUM. January 2023;6(1):89-98. doi:10.33773/jum.1202907
Chicago Güzel Ergül, Zehra. “NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES”. Journal of Universal Mathematics 6, no. 1 (January 2023): 89-98. https://doi.org/10.33773/jum.1202907.
EndNote Güzel Ergül Z (January 1, 2023) NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES. Journal of Universal Mathematics 6 1 89–98.
IEEE Z. Güzel Ergül, “NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES”, JUM, vol. 6, no. 1, pp. 89–98, 2023, doi: 10.33773/jum.1202907.
ISNAD Güzel Ergül, Zehra. “NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES”. Journal of Universal Mathematics 6/1 (January 2023), 89-98. https://doi.org/10.33773/jum.1202907.
JAMA Güzel Ergül Z. NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES. JUM. 2023;6:89–98.
MLA Güzel Ergül, Zehra. “NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES”. Journal of Universal Mathematics, vol. 6, no. 1, 2023, pp. 89-98, doi:10.33773/jum.1202907.
Vancouver Güzel Ergül Z. NEW DECOMPOSITIONS OF SOFT CONTINUITY IN SOFT TOPOLOGICAL SPACES. JUM. 2023;6(1):89-98.