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On Maximal Soft δ-open (Minimal soft δ-closed) Sets in Soft Topological Spaces

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Bishnupada Debnath
10.5120/ijca2017914378

Bishnupada Debnath. On Maximal Soft δ-open (Minimal soft δ-closed) Sets in Soft Topological Spaces. International Journal of Computer Applications 168(5):8-13, June 2017. BibTeX

@article{10.5120/ijca2017914378,
	author = {Bishnupada Debnath},
	title = {On Maximal Soft δ-open (Minimal soft δ-closed) Sets in Soft Topological Spaces},
	journal = {International Journal of Computer Applications},
	issue_date = {June 2017},
	volume = {168},
	number = {5},
	month = {Jun},
	year = {2017},
	issn = {0975-8887},
	pages = {8-13},
	numpages = {6},
	url = {http://www.ijcaonline.org/archives/volume168/number5/27869-2017914378},
	doi = {10.5120/ijca2017914378},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

In soft topological space there are some existing related concepts such as soft open, soft closed, soft subspace, soft separation axioms, soft connectedness, soft locally connectedness. In this paper, a new class of soft sets called maximal soft δ-open sets and minimal soft δ-closed sets which are fundamental results for further research are defined on soft topological space and continued in investigating the properties of these new notions of open sets with example and counter examples.

References

  1. Molodtsov, D. 1999. Soft Set theory-First results. Comput. Math. Appl. 37(4–5), 19–31.
  2. Shabir, M., Naz, M. 2011. On soft topological spaces. Comput. Math. Appl. 61, 1786–1799.
  3. Zorlutuna, I., Akdag, M., Min, W.K., Atmaca, S. 2012. Remarks on soft topological spaces. Ann. Fuzzy Math. Inf. 3(2), 171–185.
  4. Aygunoglu, A., Aygun, H: Some notes on soft topological spaces. Neural Comput. Appl. doi:10.1007/s00521-011-0722-3
  5. Chen, B. 2013. Soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci. 7(1), 287–294.
  6. Akdag, M., Ozkan, A. 2014. Soft α-open sets and soft α-continuous functions. Abstr. Anal. Appl. Art ID 891341, 1-7.
  7. Aras, C.G., Sonmez, A., Cakalli, H. On soft mappings. http:// arxiv.org/abs/1305.4545 (Submitted)
  8. Mahanta, J., Das, P.K.: On soft topological space via semiopen and semiclosed soft sets. http://arxiv.org/abs/1203.4133 (Submitted)
  9. Yumak, Y., Kaymakcı, A.K: Soft b-open sets and their aplications. http://arxiv.org /abs/1312.6964 (Submitted)
  10. Maji, P.K., Biswas, R., Roy, A.R. 2003. Soft set theory. Computers and Mathematics with Applications, Vol-45,No.4-5, pp 555–562.
  11. Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M. 2009. On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553.
  12. Arockiarani, I., Arokialancy, A. 2013. Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces. Int. J. Math. Arch. 4(2), 1–7.
  13. Kharal, A., Ahmad, B. 2011. Mappings on soft classes. New Math. Nat. Comput. 7(3), 471–481.
  14. Yumak,Y., Kaymakcı, A.K: Soft β-open sets and their aplications. http://arxiv.org /abs/1312.6964V1[Math.GN] 25 Dec 2013.
  15. Zorlutana, I.,Akdag M.,Min W.K., Atmaca S.: Remarks on Soft Topological Spaces. Annals of Fuzzy Mathematics and Informatics. 3(2),171-185(2012).
  16. Yuksel S.,Tozlu N. and Guzel Eargul Z.: Soft regular generalized closed sets in soft topological spaces, International Journal of Mathematical Analysis, 8(8) 2014, 355-367.

Keywords

Soft regular open sets, soft regular closed sets, soft δ-cluster point, soft δ-open sets, soft δ-closed sets, soft maximal open sets, soft minimal closed sets, soft maximal δ-open sets, soft minimal δ-closed sets etc.