대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권4호
  • /
  • Pages.1341-1356
  • /
  • 2018
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

SOFT SOMEWHERE DENSE SETS ON SOFT TOPOLOGICAL SPACES

  • Al-shami, Tareq M. (Department of Mathematics Faculty of Science Sana'a University)
  • 투고 : 2017.09.09
  • 심사 : 2018.05.16
  • 발행 : 2018.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

키워드

참고문헌

  1. M. Akdag and A. Ozkan, Soft $-\alpha}$-open sets and soft $-\alpha}$-continuous functions, Abstr. Appl. Anal. 2014 (2014), Art. ID 891341, 7 pp.
  2. M. Akdag and A. Ozkan, Soft b-open sets and soft b-continuous functions, Math. Sci. (Springer) 8 (2014), no. 2, Art. 124, 9 pp.
  3. M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), no. 9, 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
  4. A. Alpers, Digital topology: regular sets and root images of the cross-median filter, J. Math. Imaging Vision 17 (2002), no. 1, 7-14. https://doi.org/10.1023/A:1020766406935
  5. T. M. Al-shami, Somewhere dense sets and $ST_1$-spaces, Punjab Univ. J. Math. (Lahore) 49 (2017), no. 2, 101-111.
  6. I. Arockiarani and A. A. Lancy, Generalized soft $g{\beta}$-closed sets and soft gs${\beta}$-closed sets in soft topological spaces, Intern. J. Math. Archive 4 (2013), no.2, 1-7.
  7. A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural Computers and Applications 21 (2012), 113-119. https://doi.org/10.1007/s00521-011-0722-3
  8. B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math. Inf. Sci. 7 (2013), no. 1, 287-294. https://doi.org/10.12785/amis/070136
  9. S. Das and S. K. Samanta, Soft metric, Ann. Fuzzy Math. Inform. 6 (2013), no. 1, 77-94.
  10. M. E. El-Shafei, M. Abo-Elhamayel, and T. M. Al-shami, Partial soft separation axioms and soft compact spaces, Filomat 32 (2018), no. 4, Accepted.
  11. S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011), no. 11, 4058-4067. https://doi.org/10.1016/j.camwa.2011.09.051
  12. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, and A. M. Abd El-latif, Soft connectedness via soft ideals, J. New Results in Science 4 (2014), 90-108.
  13. D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), no. 4-5, 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  14. Sk. Nazmul and S. K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform. 6 (2013), no. 1, 1-15.
  15. D. Pei and D. Miao, From soft sets to information system, In Proceedings of the IEEE International Conference on Granular Computing 2 (2005), 617-621.
  16. R. Sahin and A. Kucuk, Soft filters and their convergence properties, Ann. Fuzzy Math. Inform. 6 (2013), no. 3, 529-543.
  17. M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011), no. 7, 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006
  18. S. Yuksel, N. Tozlu, and Z. G. Ergul, Soft filter, Math. Sci. (Springer) 8 (2014), no. 1, Art. 119, 6 pp.
  19. Y. Yumak and A. K. Kaymakci, Soft ${\beta}$-open sets and their applications, J. New Theory 4 (2015), 80-89.
  20. I. Zorlutuna, M. Akdag, W. K. Min, and S. K. Samanta, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform. 3 (2012), no. 2, 171-185.