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A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements

Year 2019, Volume: 8 Issue: 2, 53 - 66, 31.12.2019

Abstract

In this article, we study the ordinary topology on the collection of soft elements. Some interesting relations between the ordinary topology on the collection of soft elements and the soft topology are discussed. New definition of soft separation axioms and soft compactness are presented and studied using soft elements.

References

  • [1] M.Abbas, M.I.Ali, S.Romaguera, Generalized Operations in Soft Set Theory via Relaxed Conditions on Parameters, Filomat, 19 (2017), 5955-5964.
  • [2] U.Acar, F.Koyuncu, B.Tanay, Soft sets and soft rings, Computers and mathematics with Applications, 59 (2010), 3458-3463.
  • [3] H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 177 (2007), 2726-2735.
  • [4] M.A.K.Al-Khafaj, M.H.Mahmood, Some Properties of Soft Connected Space and Soft Locally Connected Spaces, IOSR Journal of Mathematics, 10 (2014), 102-107.
  • [5] S.S.Benchalli, P.G.Patil, Some Properties of Soft Beta-Compact and Related Soft Topological Spaces, Italian Journal of Pure and Applied Mathematics, 38 (2017), 487-496.
  • [6] N.Cagman, S.Karatas, S.Enginogiu, Soft Topology, Computers and mathematics with Applications, 61 (2011), 351-358.
  • [7] Y.Celik, C.Ekiz and S.Yamak, A new view on soft rings, Hacettepe Journal of Mathematics and Statistics, 40 (2011), 273-286.
  • [8] F.Feng, Y.B.Jun, X.Zhao, Soft Semirings, Computers and mathematics with Applications, 56 (2008), 2621-2628.
  • [9] D.N.Georgiou, A.C.Megaritis and V.I.Petropoulos, On Soft Topological Spaces, Appl. Math. Inf. Sci. 7 (2013), 1889-1901.
  • [10] D.N.Georgiou, A.C.Megaritis Soft Set Theory and Topology, Appl.Gen.Topo. 15 (2014), 93-109.
  • [11] S.Goldar, S.Ray, A Study of Soft Topology from Classical View Point , Proceedings of IMBIC, 6 (2017), 108-116.
  • [12] S.Goldar, S.Ray, On Soft Ring And Soft Ideal, Communicated to The Journal of Mathematical Journal of Interdisciplinary Sciences.
  • [13] A.M.Hamza, M.Saad, On The Open Limit Point Compactness and Soft Open Limit Point Compactness, Applied Mathematical sciences, 11 (2017), 2697-2706.
  • [14] Takanori Hida, A comparison of two formulations of soft compactness, Annals of Fuzzy Mathematics and Informatics, 8 (2014), 511-525.
  • [15] R.A.Hosny, A.M.Abd El-Latif, Soft G-compactness in Soft Topological Spaces, Annals of Fuzzy Math. and Info., 11 (2016), 973-987.
  • [16] S.Hussain A note on Soft connectedness, Journal of the Egyptian Mathematical Society 23 (2015), 6-11.
  • [17] S.Jalil, B.S.Reddy, On Soft Compact, Sequentially Compact and Locally Compactness Advances in Fuzzy Mathematics, 12 (2017), 835-844.
  • [18] A.Kandil, O.A.E.Tantawy, S.A.El-Sheikh, A.M.Abd El-Latif Soft Connectedness Via Soft Ideals, Journal of New Results in Sciences, 4(2014), 90-108.
  • [19] P.K.Maji, R.Biswas and A.R.Roy, Soft Set Theory, Computers and mathematics with Applications, 45 (2003), 555-562.
  • [20] P.Majumdar, S.K.Samanta, On Soft Mapping Computers and mathematics with Applications, 60 (2010), 2666-2672.
  • [21] D.Molodtsov, Soft set theory - First results, Computers and mathematics with Applications, 37(4/5) (1999), 19-31.
Year 2019, Volume: 8 Issue: 2, 53 - 66, 31.12.2019

Abstract

References

  • [1] M.Abbas, M.I.Ali, S.Romaguera, Generalized Operations in Soft Set Theory via Relaxed Conditions on Parameters, Filomat, 19 (2017), 5955-5964.
  • [2] U.Acar, F.Koyuncu, B.Tanay, Soft sets and soft rings, Computers and mathematics with Applications, 59 (2010), 3458-3463.
  • [3] H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 177 (2007), 2726-2735.
  • [4] M.A.K.Al-Khafaj, M.H.Mahmood, Some Properties of Soft Connected Space and Soft Locally Connected Spaces, IOSR Journal of Mathematics, 10 (2014), 102-107.
  • [5] S.S.Benchalli, P.G.Patil, Some Properties of Soft Beta-Compact and Related Soft Topological Spaces, Italian Journal of Pure and Applied Mathematics, 38 (2017), 487-496.
  • [6] N.Cagman, S.Karatas, S.Enginogiu, Soft Topology, Computers and mathematics with Applications, 61 (2011), 351-358.
  • [7] Y.Celik, C.Ekiz and S.Yamak, A new view on soft rings, Hacettepe Journal of Mathematics and Statistics, 40 (2011), 273-286.
  • [8] F.Feng, Y.B.Jun, X.Zhao, Soft Semirings, Computers and mathematics with Applications, 56 (2008), 2621-2628.
  • [9] D.N.Georgiou, A.C.Megaritis and V.I.Petropoulos, On Soft Topological Spaces, Appl. Math. Inf. Sci. 7 (2013), 1889-1901.
  • [10] D.N.Georgiou, A.C.Megaritis Soft Set Theory and Topology, Appl.Gen.Topo. 15 (2014), 93-109.
  • [11] S.Goldar, S.Ray, A Study of Soft Topology from Classical View Point , Proceedings of IMBIC, 6 (2017), 108-116.
  • [12] S.Goldar, S.Ray, On Soft Ring And Soft Ideal, Communicated to The Journal of Mathematical Journal of Interdisciplinary Sciences.
  • [13] A.M.Hamza, M.Saad, On The Open Limit Point Compactness and Soft Open Limit Point Compactness, Applied Mathematical sciences, 11 (2017), 2697-2706.
  • [14] Takanori Hida, A comparison of two formulations of soft compactness, Annals of Fuzzy Mathematics and Informatics, 8 (2014), 511-525.
  • [15] R.A.Hosny, A.M.Abd El-Latif, Soft G-compactness in Soft Topological Spaces, Annals of Fuzzy Math. and Info., 11 (2016), 973-987.
  • [16] S.Hussain A note on Soft connectedness, Journal of the Egyptian Mathematical Society 23 (2015), 6-11.
  • [17] S.Jalil, B.S.Reddy, On Soft Compact, Sequentially Compact and Locally Compactness Advances in Fuzzy Mathematics, 12 (2017), 835-844.
  • [18] A.Kandil, O.A.E.Tantawy, S.A.El-Sheikh, A.M.Abd El-Latif Soft Connectedness Via Soft Ideals, Journal of New Results in Sciences, 4(2014), 90-108.
  • [19] P.K.Maji, R.Biswas and A.R.Roy, Soft Set Theory, Computers and mathematics with Applications, 45 (2003), 555-562.
  • [20] P.Majumdar, S.K.Samanta, On Soft Mapping Computers and mathematics with Applications, 60 (2010), 2666-2672.
  • [21] D.Molodtsov, Soft set theory - First results, Computers and mathematics with Applications, 37(4/5) (1999), 19-31.
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sujay Goldar

Subhasis Ray This is me

Publication Date December 31, 2019
Published in Issue Year 2019 Volume: 8 Issue: 2

Cite

APA Goldar, S., & Ray, S. (2019). A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements. Journal of New Results in Science, 8(2), 53-66.
AMA Goldar S, Ray S. A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements. JNRS. December 2019;8(2):53-66.
Chicago Goldar, Sujay, and Subhasis Ray. “A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements”. Journal of New Results in Science 8, no. 2 (December 2019): 53-66.
EndNote Goldar S, Ray S (December 1, 2019) A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements. Journal of New Results in Science 8 2 53–66.
IEEE S. Goldar and S. Ray, “A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements”, JNRS, vol. 8, no. 2, pp. 53–66, 2019.
ISNAD Goldar, Sujay - Ray, Subhasis. “A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements”. Journal of New Results in Science 8/2 (December 2019), 53-66.
JAMA Goldar S, Ray S. A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements. JNRS. 2019;8:53–66.
MLA Goldar, Sujay and Subhasis Ray. “A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements”. Journal of New Results in Science, vol. 8, no. 2, 2019, pp. 53-66.
Vancouver Goldar S, Ray S. A Study of Soft Topological Axioms and Soft Compactness by Using Soft Elements. JNRS. 2019;8(2):53-66.


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