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).
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).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | January 31, 2023 |
| Submission Date | November 11, 2022 |
| Acceptance Date | January 30, 2023 |
| Published in Issue | Year 2023 Volume: 6 Issue: 1 |
