Skip to main content
SpringerLink
Log in

On soft compact and soft Lindelöf spaces via soft regular closed sets

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this work, the notion of \(\hbox {soft}_{\mathfrak {int}}\)-compact and \(\hbox {soft}_{\mathfrak {int}}\)-Lindelöf spaces are initiated and studied. We present some of their properties and give some characterizations of them. Also, we establish the relationships between them and some other known soft spaces with the help of examples, and study them with respect to the finite and countable additive properties. In addition, we reveal the relationships between soft topology and classical (parametric) topology. Finally, we study the behaviours of \(\hbox {soft}_{\mathfrak {int}}\)-compact and \(\hbox {soft}_{\mathfrak {int}}\)-Lindelöf spaces under some soft mappings as well as we prove that they are topological properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akdag, M., Ozkan, A.: Soft \(\alpha \)-open sets and soft \(\alpha \)-continuous functions. Abstr. Appl. Anal. Art ID 891341, 1–7 (2014)

    Article  MathSciNet  Google Scholar 

  2. Alcantud, J.C.R.: Soft open bases and a novel construction of soft topologies from bases for topologies. Mathematics (2020). https://doi.org/10.3390/math8050672

    Article  Google Scholar 

  3. Alcantud, J.C.R., García, G.S.: A new criterion for soft set based decision making problems under incomplete information. Int. J. Comput. Intell. Syst. 10, 394–404 (2017)

    Article  Google Scholar 

  4. Ali, M.I., Feng, F., Liu, X., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)

    Article  MathSciNet  Google Scholar 

  5. Al-shami, T.M.: Soft somewhere dense sets on soft topological spaces. Commun. Korean Math. Soc. 33(4), 1341–1356 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Al-shami, T.M.: Comment on “soft mappings space”. Sci. World J. 2019, 6903809 (2019). https://doi.org/10.1155/2019/6903809

  7. Al-shami, T.M.: Investigation and corrigendum to some results related to \(g\)-soft equality and \(gf\)-soft equality relations. Filomat 33(11), 3375–3383 (2019)

    Article  MathSciNet  Google Scholar 

  8. Al-shami, T.M.: Comments on some results related to soft separation axioms. Afr. Mat. 31(7), 1105–1119 (2020)

    Article  MathSciNet  Google Scholar 

  9. Al-shami, T.M., Mhemdi, A., Rawshdeh, A.A., Al-Jarrah, H.H.: Soft version of compact and Lindelöf spaces using soft somewhere dense sets. AIMS Math. 6(8), 8064–8077 (2021)

    Article  MathSciNet  Google Scholar 

  10. Al-shami, T.M., Al-Shumrani, M.A., Asaad, B.A.: Some generalized forms of soft compactness and soft Lindelöfness via soft \(\alpha \)-open sets. Ital. J. Pure Appl. Math. 43, 680–704 (2020)

    Google Scholar 

  11. Al-shami, T.M., El-Shafei, M.E.: Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone. Soft Comput. 24(7), 5377–5387 (2020)

    Article  Google Scholar 

  12. Al-shami, T.M., El-Shafei, M.E., Abo-Elhamayel, M.: Almost soft compact and approximately soft Lindelöf spaces. J. Taibah Univ. Sci. 12(5), 620–630 (2018)

    Article  Google Scholar 

  13. Al-shami, T.M., El-Shafei, M.E.: On soft compact and soft Lindelöf spaces via soft pre-open sets. Ann. Fuzzy Math. Inform. 17(1), 79–100 (2019)

    Article  MathSciNet  Google Scholar 

  14. Al-shami, T.M., El-Shafei, M.E.: \(T\)-soft equality relation. Turk. J. Math. 44(4), 1427–1441 (2020)

    Article  MathSciNet  Google Scholar 

  15. Al-shami, T.M., El-Shafei, M.E., Abo-Elhamayel, M.: Seven generalized types of soft semi-compact spaces. Korean J. Math. 27(3), 661–690 (2019)

    MathSciNet  MATH  Google Scholar 

  16. Al-shami, T.M., Kočinac, L.D.R.: The equivalence between the enriched and extended soft topologies. Appl. Comput. Math. 18(2), 149–162 (2019)

    MathSciNet  MATH  Google Scholar 

  17. Al-shami, T.M., Kočinac, L.D.R.: Nearly soft Menger spaces. J. Math. 2020, 3807418 (2020). https://doi.org/10.1155/2020/3807418

  18. Al-shami, T.M., Kočinac, L.D.R., Asaad, B.A.: Sum of soft topological spaces. Mathematics 8(6), 990 (2020). https://doi.org/10.3390/math8060990

    Article  Google Scholar 

  19. Asaad, B.A.: Results on soft extremally disconnectedness of soft topological spaces. J. Math. Comput. Sci. 17, 448–464 (2017)

    Article  Google Scholar 

  20. Aygünoǧlu, A., Aygün, H.: Some notes on soft topological spaces. Neural Comput. Appl. 21, 113–119 (2012)

    Article  Google Scholar 

  21. Debnath, B.: A note on soft nearly compact and soft nearly paracompactness in soft topological spaces. Int. J. Innov. Res. Sci. Eng. Technol. 6(8), 15906–15914 (2017)

    Google Scholar 

  22. Caǧman, N., Enginoǧlu, S.: Soft matrix theory and its decision making. Comput. Math. Appl. 59, 3308–3314 (2010)

    Article  MathSciNet  Google Scholar 

  23. Chen, B.: Soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci. 7(1), 287–294 (2013)

    Article  MathSciNet  Google Scholar 

  24. Das, S., Samanta, S.K.: Soft metric. Ann. Fuzzy Math. Inform. 1, 77–94 (2013)

    MathSciNet  MATH  Google Scholar 

  25. El-Shafei, M.E., Abo-Elhamayel, M., Al-shami, T.M.: Partial soft separation axioms and soft compact spaces. Filomat 32(13), 4755–4771 (2018)

    Article  MathSciNet  Google Scholar 

  26. El-Shafei, M.E., Al-shami, T.M.: Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Comput. Appl. Math. (2020). https://doi.org/10.1007/s40314-020-01161-3

    Article  MathSciNet  MATH  Google Scholar 

  27. Hida, T.: A comparison of two formulations of soft compactness. Ann. Fuzzy Math. Inform. 8(4), 511–524 (2014)

    MathSciNet  MATH  Google Scholar 

  28. Hussain, S.: A note on soft connectedness. J. Egypt Math. Soc. 23, 6–11 (2005)

    Article  MathSciNet  Google Scholar 

  29. Hussain, S., Ahmad, B.: Some properties of soft topological spaces. Comput. Math. Appl. 62, 4058–4067 (2011)

    Article  MathSciNet  Google Scholar 

  30. Ilango, G., Ravindran, M.: On soft preopen sets in soft topological spaces. Int. J. Math. Res. 5(4), 399–409 (2013)

    Google Scholar 

  31. Kharal, A., Ahmed, B.: Mappings on soft classes. New Math. Nat. Comput. 7(3), 471–481 (2011)

    Article  MathSciNet  Google Scholar 

  32. Kočinac, L.D.R., Al-shami, T.M., Vildan, Ç.: Selection principles in the context of soft sets: Menger spaces. Soft Comput. 25(20), 12693–12702 (2021)

    Article  Google Scholar 

  33. Maji, P.K., Biswas, R., Roy, R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)

    Article  MathSciNet  Google Scholar 

  34. Min, W.K.: A note on soft topological spaces. Comput. Math. Appl. 61, 3524–3528 (2011)

    Article  MathSciNet  Google Scholar 

  35. Mahanta, J., Das, P.K.: On soft topological space via semiopen and semiclosed soft sets. Kyungpook Math. J. 54(2), 221–236 (2014)

    Article  MathSciNet  Google Scholar 

  36. Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)

    Article  MathSciNet  Google Scholar 

  37. Nazmul, S., Samanta, S.K.: Neighbourhood properties of soft topological spaces. Ann. Fuzzy Math. Inform. 1, 1–15 (2013)

    MathSciNet  MATH  Google Scholar 

  38. Ozkan, A., Akdag, M., Erol, F.: Soft \(b\)-compact spaces. New Trends Math. Sci. 4(2), 211–219 (2016)

    Article  MathSciNet  Google Scholar 

  39. Rawshdeh, A.A., Al-Jarrah, H.H., Al-shami, T.M.: Soft expandable spaces (submitted)

  40. Shabir, M., Naz, M.: On soft topological spaces. Comput. Math. Appl. 61, 1786–1799 (2011)

    Article  MathSciNet  Google Scholar 

  41. Singh, A., Noorie, N.S.: Remarks on soft axioms. Ann. Fuzzy Math. Inform. 14(5), 503–513 (2017)

    Article  MathSciNet  Google Scholar 

  42. Terepeta, M.: On separating axioms and similarity of soft topological spaces. Soft Comput. 23(3), 1049–1057 (2019)

    Article  Google Scholar 

  43. Yüksel, Ş, Tozlu, N., Ergül, Z.G.: Soft regular generalized closed sets in soft topological spaces. Int. J. Math. Anal. 8(8), 355–367 (2014)

    Article  MathSciNet  Google Scholar 

  44. Yumak, Y., Kaymakci, A.K.: Soft \(\beta \)-open sets and their applications. J. New Theory 4, 80–89 (2015)

    Google Scholar 

  45. Zorlutuna, I., Akdag, M., Min, W.K., Atmaca, S.: Remarks on soft topological spaces. Ann. Fuzzy Math. Inform. 2, 171–185 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, Jordan

    Heyam H. Al-jarrah

  2. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, Jordan

    Amani Rawshdeh

  3. Department of Mathematics, Faculty of Science, Sana’a University, Sana’a, Yemen

    Tareq M. Al-shami

Authors
  1. Heyam H. Al-jarrah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amani Rawshdeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tareq M. Al-shami
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors contributed to each part of this paper equally. The authors read and approved the final manuscript.

Corresponding author

Correspondence to Heyam H. Al-jarrah.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-jarrah, H.H., Rawshdeh, A. & Al-shami, T.M. On soft compact and soft Lindelöf spaces via soft regular closed sets. Afr. Mat. 33, 23 (2022). https://doi.org/10.1007/s13370-021-00952-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13370-021-00952-z

Keywords

Mathematics Subject Classification

Search

Navigation