Soft ξ-open sets in Soft Topological Spaces
DOI:
https://doi.org/10.25271/sjuoz.2019.7.3.598Keywords:
Soft topology, soft continuous, ξ-open setAbstract
The objective of studing the current paper is to introduced a new class of soft open sets in soft topological spaces called soft -open sets. Then soft -open sets are used to study some soft topological concepts. Furthermore, the concept of soft -continuous and almost soft -continuous functions are defined by using the soft -open sets. Some properties and Characterizations of such functions are given.
References
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Aygünoğlu, A., & Aygün, H. (2012). Some notes on soft topological spaces. Neural computing and Applications, 21(1), 113-119.
Çağman, N., Karataş, S., & Enginoglu, S. (2011). Soft topology. Computers & Mathematics with Applications, 62(1), 351-358.
Chen, B. (2013). Soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci, 7(1), 287-294.
El-Monsef, M. A., & El-Deeb, S. (1982). On pre-continuous and weak pre-continuous mappings. proc. Mth. Phys. Soc. Egypt, 53(1), 47-53.
Georgiou, D., Megaritis, A., & Petropoulos, V. (2013). On soft topological spaces. Applied Mathematics & Information Sciences, 7(5), 1889-1901.
Georgiou, D. N., & Megaritis, A. (2014). Soft set theory and topology. Applied General Topology, 15(1), 93-109.
Hasan, H. M. (2010). On Some Types of Continuity, Separation Axioms and Dimension Functions. Duhok University Ph.D Thesis.
Hussain, S. (2014). Properties of soft semi-open and soft semi-closed sets. arXiv preprint arXiv:1409.3459.
Hussain, S., & Ahmad, B. (2011). Some properties of soft topological spaces. Computers & Mathematics with Applications, 62(11), 4058-4067. doi: http://dx.doi.org/10.1016/j.camwa.2011.09.051
Kharal, A., & Ahmad, B. (2011). Mappings on soft classes. New Mathematics and Natural Computation, 7(03), 471-481.
Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70(1), 36-41.
Mahanta, J., & Das, P. K. (2012). On soft topological space via semiopen and semiclosed soft sets. arXiv preprint arXiv, 1203.4133.
Molodtsov, D. (1999). Soft set theory—first results. Computers & Mathematics with Applications, 37(4), 19-31.
Nazmul, S., & Samanta, S. (2012). Neighbourhood properties of soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 6, 1-15.
Njȧstad, O. (1965). On some classes of nearly open sets. Pacific Journal of mathematics, 15(3), 961-970.
Ramadhan, M., Abed., & Sayed, O., R. (2018). Some Properties of Soft Delta-Topology. Academic Journal of Nawroz University (AJNU), 8(3), 1-16.
Shabir, M., & Naz, M. (2011). On soft topological spaces. Computers & Mathematics with Applications, 61(7), 1786-1799.
Yuksel, S., Tozlu, N., & Ergul, Z. G. (2014). Soft regular generalized closed sets in soft topological spaces. Int. Journal of Math. Analysis, 8(8), 355-367.
Yumak, Y., & Kaymakcı, A. K. (2013). Soft {\beta}-Open Sets And Their Applications. arXiv preprint arXiv:1312.6964.
Zorlutuna, I., Akdag, M., Min, W., & Atmaca, S. (2012). Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3(2), 171-185.
Akdag, M., & Ozkan, A. (2014a). Soft-open sets and soft-continuous functions. Paper presented at the Abstract and Applied Analysis.
Akdag, M., & Ozkan, A. (2014b). Soft b-open sets and soft b-continuous functions. Mathematical Sciences, 8(2), 1-9.
Alias, B. K., & Baravan, A. A. (2009). Ps-open sets and Ps-continuity in topological spaces. Journal of Duhok University, 12(2), 183-192.
Alias, B. K., & Zanyar, A. A. (2010). sc-Open sets and sc-Continuity in topological spaces. Journal of Advanced Research in Pure Mathematics, 2(3), 87-101.
Allam, A. A., Ismail, T. H., & Muhammed, R. A. (2017). A new approach to soft belonging. Journal of Annals of Fuzzy Mathematics and Informatics, 13(1), 145-152.
Aygünoğlu, A., & Aygün, H. (2012). Some notes on soft topological spaces. Neural computing and Applications, 21(1), 113-119.
Çağman, N., Karataş, S., & Enginoglu, S. (2011). Soft topology. Computers & Mathematics with Applications, 62(1), 351-358.
Chen, B. (2013). Soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci, 7(1), 287-294.
El-Monsef, M. A., & El-Deeb, S. (1982). On pre-continuous and weak pre-continuous mappings. proc. Mth. Phys. Soc. Egypt, 53(1), 47-53.
Georgiou, D., Megaritis, A., & Petropoulos, V. (2013). On soft topological spaces. Applied Mathematics & Information Sciences, 7(5), 1889-1901.
Georgiou, D. N., & Megaritis, A. (2014). Soft set theory and topology. Applied General Topology, 15(1), 93-109.
Hasan, H. M. (2010). On Some Types of Continuity, Separation Axioms and Dimension Functions. Duhok University Ph.D Thesis.
Hussain, S. (2014). Properties of soft semi-open and soft semi-closed sets. arXiv preprint arXiv:1409.3459.
Hussain, S., & Ahmad, B. (2011). Some properties of soft topological spaces. Computers & Mathematics with Applications, 62(11), 4058-4067. doi: http://dx.doi.org/10.1016/j.camwa.2011.09.051
Kharal, A., & Ahmad, B. (2011). Mappings on soft classes. New Mathematics and Natural Computation, 7(03), 471-481.
Levine, N. (1963). Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70(1), 36-41.
Mahanta, J., & Das, P. K. (2012). On soft topological space via semiopen and semiclosed soft sets. arXiv preprint arXiv, 1203.4133.
Molodtsov, D. (1999). Soft set theory—first results. Computers & Mathematics with Applications, 37(4), 19-31.
Nazmul, S., & Samanta, S. (2012). Neighbourhood properties of soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 6, 1-15.
Njȧstad, O. (1965). On some classes of nearly open sets. Pacific Journal of mathematics, 15(3), 961-970.
Ramadhan, M., Abed., & Sayed, O., R. (2018). Some Properties of Soft Delta-Topology. Academic Journal of Nawroz University (AJNU), 8(3), 1-16.
Shabir, M., & Naz, M. (2011). On soft topological spaces. Computers & Mathematics with Applications, 61(7), 1786-1799.
Yuksel, S., Tozlu, N., & Ergul, Z. G. (2014). Soft regular generalized closed sets in soft topological spaces. Int. Journal of Math. Analysis, 8(8), 355-367.
Yumak, Y., & Kaymakcı, A. K. (2013). Soft {\beta}-Open Sets And Their Applications. arXiv preprint arXiv:1312.6964.
Zorlutuna, I., Akdag, M., Min, W., & Atmaca, S. (2012). Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3(2), 171-185.
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Published
2019-09-30
How to Cite
Mohammed, R. A., & Ameen, R. S. (2019). Soft ξ-open sets in Soft Topological Spaces. Science Journal of University of Zakho, 7(3), 108–119. https://doi.org/10.25271/sjuoz.2019.7.3.598
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Science Journal of University of Zakho
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