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Year 2017, Issue: 19, 82 - 107, 24.12.2017

Arif Mehmood Khattak , Asad Zaighum Muhammad Ishfaq Shamoona Jbeen Iqrar Hussain

Abstract

References

  • [1] B. M. Ittanagi, 2014, soft bi-topological spaces, International Journal of Computer Application (0975 8887), v107-No. 7.
  • [2] S. A El-Sheikh, Rodyna A. Hosny and A. M. Abd-e-Latif, 2015, Characterization of b soft separation Axioms in soft topological spaces in Inf. Sci. Let t. 4 (3) 125-133.
  • [3] M. Naz, M. Shabir and M. I. Ali, 2015, Separation axiom in bi soft topological spaces, Arxiv. 1850 of . 00866 vl [Math, GN]
  • [4] D. A Molodtsov, 1999, soft set theory first results, Comp. Math. Appl., 37, 19-31.
  • [5] J. C. Kelly, 1963, Bitopological spaces proc London math-soc, 13, 71-81.
  • [6] P. K. Maji, R, Biswas and A. R. Roy, 2003, soft set theory, Comp. Math. Appl., 45, 555-562.
  • [7] M. Shabir and M. Naz, on soft topological space , 2011, Comp. Math. Appl., 61, 1786-1799.
  • [8] H. Aktas and N. Cagman, 2007, soft sets and soft groups, Inform. Sci 1 (77), 2726- 2735.
  • [9] Chen, 2005, the paramatrization reduction of soft sets and application,Comp. Math, Appl., 49,757-763.
  • [10] F. Feng, Y. B. Jun, X. Z. Zhao, 2008, soft semi rings, Comp. Math. Appl., 56, 2621- 2628
  • [11] Z. Kong, L. Gao, L. Wang, S. Li, 2008, The normal parameter reduction of soft set and its algorithm. Comp., Math. Appl., 56, 3029-3027.
  • [12] Y. B. Jun, C. H. Park, 2008, Application of soft sets and ideal theory of BCK/BCIalgebra, Inf, Sci 178, 2466-2475.
  • [13] Pie and D. Miao, 2005, Form soft sets to information system,in X. Hu, Q. Liu,A. Skowron, T. Y . Lin, R. R. Yager, B. Zhang (Eds), Proceedings of Granular Computing,Vol. 2,IEEE,pp. 617-621.
  • [14] Majumdar and S. K Samanta, 2010, on soft mapping, Comp. Math. Appl., 60, 2666- 2672.
  • [15] B. Jun, 2008, soft BSK/BCI-algehra, Comp. Math. Appl., 56, 1408-1413.
  • [16] Shahir and M. I. Ali, 2009) soft ideals and generalized fuzzy ideals in semigroups, New Math. Wat. Comp. 5,599-615
  • [17] Y. Zou and Z. Xiao, 2008, Data analysis approach of soft sets under incomp Let e information, Knowledge-Based System, 21, 941-945.
  • [18] A. Aygunoglu and H. Aygun, Some notes on soft topological space , Neural Comp and Applic DoI 10. 1007/s. 00521-011-0722-3.
  • [19] Husain, B Ahmad, 2011, Some properties of soft topological spaces, Comp. Math. App., 62, 4058-4067.
  • [20] D. N Geogiou, A. C Megart is, V. I. 2013, petropounlos On soft topological spaces, Appl, Math. Inf, Sci 7 (2), 1889-190
  • [21] Hen B, 2013, soft semi open sets and related properties in soft topological spaces. Appl, math, Inf, sci 7 (1), 287-294.
  • [22] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Lat if, 2015,g operation and decomposition of some form of soft continuity of soft topological spaces via soft ideal, Ann Fuzzy Math, inf, 9 (3),385-402.
  • [23] A. Kandil, O. A . E. Tantawy, S. A, EI Sheikh and A. M, Abd-e-Latif, 2014, soft connectedness via soft ideal, Journal of New result in science, 4,90-108.
  • [24] A. Kandil, O. A . E. Tantawy, S. A, EI Sheikh and A. M, Abd-e-Latif, 2014, soft ideal theory, soft local function and generalize soft topological spaces, Appl. Math. Inf. Sci, 8 (4),1595-1603.
  • [25] A. Kandil. O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2015, soft regular ity and normality based on semi open soft sets and soft ideals,App. Math. Inf. Sci. Let t, 3,47-55.
  • [26] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014) soft semi compactness, via soft ideals, Appl. Math . Inf. Sci, 8 (5),2297-2306
  • [27] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014) soft semi (Quasi) husdorff spaces via soft ideals, South Asian, J. Math, 4 (6),265-284.
  • [28] I. Zorlutana,N. Akdog,W. K. Min, S. Atmaca, 2012, Remarks on soft topological spaces, Annals, of Fuzzy Mathematics and informatics 3 (2),171-185
  • [29] J. Mahanta. P. K. Das, 2012, On soft topological spaces Via semi open and semi closed soft sets, ar XIV 1203. 1433VI [math, G. N]
  • [30] A. Kandil’O. A. E. Tantawy, S. A El-Sheikh and A. M Abd-Latif, 2014, Sopra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces Appl. Math . Inf. Sci, (4), 1731-1740.
  • [31] S. A El-Sheikh and A. M Abd-e-Latif, 2014, Decomposition of some type of supra soft sets and soft continuity, international journal of mathematics trends and technology, 9 (1), 37-56.
  • [32] L. A. Zadeh, 1965, Fuzzy sets, information and control 8,338-353.
  • [33] Q. M. Sun, Z. L Zhang, J. Liu soft sets and soft modules, proceeding of rough sets and Knowledge technology, third international conference, RSKT 2008,17-19 May, Chengdu, Chaina, PP 403-409, 2008.
  • [34] C. H. Park, Y. B. Jun, M. A. Ozturk, 2008, soft WS Algebras, Communications of the Korean Mathematical Society 23 (3), 313-324.
  • [35] I. Arockiarani and A. A. Lancy, 2013, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces, IJMRS, 4 (2), 1-7.
  • [36] B. Chen, 2013, soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci, 7 (1), 287-294.
  • [37] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, 1982, A note on semicontinuity and pre-continuity. Indian J. Pure Appl. Math. 13 (10), 1119-1123.
  • [38] S. Hussain, B. Ahmad, 2015, soft separation axioms in soft topological space submitted to elsvier.
  • [39] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014, soft semi separation axioms and some
  • [40] U. D. Tapi,Ranu Sharma,Bhagyashri A. Deole, 2014, Separation Axioms in Quad topological spaces, Bul Let in of Mathematical Science and Applications İS SN 2278-9634, Vol. 10, pp 16-18.
  • [41] N. F. Hameed and Yahya Abid, 2011,Certain types of separation axioms in Tritopological spaces,Iraqi Journal of science,Vol 52,No. 2,PP212-217.
  • [42] Y. Yumak and A. K. Kaymaci, 2015, some β-Open sets and their Applications, journal of New Theory, 4 (2015) 80-89.

SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES

Year 2017, Issue: 19, 82 - 107, 24.12.2017

Arif Mehmood Khattak , Asad Zaighum Muhammad Ishfaq Shamoona Jbeen Iqrar Hussain

Abstract

Our main interest in this study is to look for soft regular separations axioms in soft quad topological spaces. We talk over and focus our attention on soft regular separation axioms in soft quad topological spaces with respect to ordinary points and soft points. Moreover study the inherited characteristics at different angles with respect to ordinary points and soft points. Some of their central properties in soft quad topological spaces are also brought under examination.

Keywords

Soft sets soft topology soft regular open set soft regular closed set soft quad topological space

References

  • [1] B. M. Ittanagi, 2014, soft bi-topological spaces, International Journal of Computer Application (0975 8887), v107-No. 7.
  • [2] S. A El-Sheikh, Rodyna A. Hosny and A. M. Abd-e-Latif, 2015, Characterization of b soft separation Axioms in soft topological spaces in Inf. Sci. Let t. 4 (3) 125-133.
  • [3] M. Naz, M. Shabir and M. I. Ali, 2015, Separation axiom in bi soft topological spaces, Arxiv. 1850 of . 00866 vl [Math, GN]
  • [4] D. A Molodtsov, 1999, soft set theory first results, Comp. Math. Appl., 37, 19-31.
  • [5] J. C. Kelly, 1963, Bitopological spaces proc London math-soc, 13, 71-81.
  • [6] P. K. Maji, R, Biswas and A. R. Roy, 2003, soft set theory, Comp. Math. Appl., 45, 555-562.
  • [7] M. Shabir and M. Naz, on soft topological space , 2011, Comp. Math. Appl., 61, 1786-1799.
  • [8] H. Aktas and N. Cagman, 2007, soft sets and soft groups, Inform. Sci 1 (77), 2726- 2735.
  • [9] Chen, 2005, the paramatrization reduction of soft sets and application,Comp. Math, Appl., 49,757-763.
  • [10] F. Feng, Y. B. Jun, X. Z. Zhao, 2008, soft semi rings, Comp. Math. Appl., 56, 2621- 2628
  • [11] Z. Kong, L. Gao, L. Wang, S. Li, 2008, The normal parameter reduction of soft set and its algorithm. Comp., Math. Appl., 56, 3029-3027.
  • [12] Y. B. Jun, C. H. Park, 2008, Application of soft sets and ideal theory of BCK/BCIalgebra, Inf, Sci 178, 2466-2475.
  • [13] Pie and D. Miao, 2005, Form soft sets to information system,in X. Hu, Q. Liu,A. Skowron, T. Y . Lin, R. R. Yager, B. Zhang (Eds), Proceedings of Granular Computing,Vol. 2,IEEE,pp. 617-621.
  • [14] Majumdar and S. K Samanta, 2010, on soft mapping, Comp. Math. Appl., 60, 2666- 2672.
  • [15] B. Jun, 2008, soft BSK/BCI-algehra, Comp. Math. Appl., 56, 1408-1413.
  • [16] Shahir and M. I. Ali, 2009) soft ideals and generalized fuzzy ideals in semigroups, New Math. Wat. Comp. 5,599-615
  • [17] Y. Zou and Z. Xiao, 2008, Data analysis approach of soft sets under incomp Let e information, Knowledge-Based System, 21, 941-945.
  • [18] A. Aygunoglu and H. Aygun, Some notes on soft topological space , Neural Comp and Applic DoI 10. 1007/s. 00521-011-0722-3.
  • [19] Husain, B Ahmad, 2011, Some properties of soft topological spaces, Comp. Math. App., 62, 4058-4067.
  • [20] D. N Geogiou, A. C Megart is, V. I. 2013, petropounlos On soft topological spaces, Appl, Math. Inf, Sci 7 (2), 1889-190
  • [21] Hen B, 2013, soft semi open sets and related properties in soft topological spaces. Appl, math, Inf, sci 7 (1), 287-294.
  • [22] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Lat if, 2015,g operation and decomposition of some form of soft continuity of soft topological spaces via soft ideal, Ann Fuzzy Math, inf, 9 (3),385-402.
  • [23] A. Kandil, O. A . E. Tantawy, S. A, EI Sheikh and A. M, Abd-e-Latif, 2014, soft connectedness via soft ideal, Journal of New result in science, 4,90-108.
  • [24] A. Kandil, O. A . E. Tantawy, S. A, EI Sheikh and A. M, Abd-e-Latif, 2014, soft ideal theory, soft local function and generalize soft topological spaces, Appl. Math. Inf. Sci, 8 (4),1595-1603.
  • [25] A. Kandil. O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2015, soft regular ity and normality based on semi open soft sets and soft ideals,App. Math. Inf. Sci. Let t, 3,47-55.
  • [26] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014) soft semi compactness, via soft ideals, Appl. Math . Inf. Sci, 8 (5),2297-2306
  • [27] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014) soft semi (Quasi) husdorff spaces via soft ideals, South Asian, J. Math, 4 (6),265-284.
  • [28] I. Zorlutana,N. Akdog,W. K. Min, S. Atmaca, 2012, Remarks on soft topological spaces, Annals, of Fuzzy Mathematics and informatics 3 (2),171-185
  • [29] J. Mahanta. P. K. Das, 2012, On soft topological spaces Via semi open and semi closed soft sets, ar XIV 1203. 1433VI [math, G. N]
  • [30] A. Kandil’O. A. E. Tantawy, S. A El-Sheikh and A. M Abd-Latif, 2014, Sopra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces Appl. Math . Inf. Sci, (4), 1731-1740.
  • [31] S. A El-Sheikh and A. M Abd-e-Latif, 2014, Decomposition of some type of supra soft sets and soft continuity, international journal of mathematics trends and technology, 9 (1), 37-56.
  • [32] L. A. Zadeh, 1965, Fuzzy sets, information and control 8,338-353.
  • [33] Q. M. Sun, Z. L Zhang, J. Liu soft sets and soft modules, proceeding of rough sets and Knowledge technology, third international conference, RSKT 2008,17-19 May, Chengdu, Chaina, PP 403-409, 2008.
  • [34] C. H. Park, Y. B. Jun, M. A. Ozturk, 2008, soft WS Algebras, Communications of the Korean Mathematical Society 23 (3), 313-324.
  • [35] I. Arockiarani and A. A. Lancy, 2013, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces, IJMRS, 4 (2), 1-7.
  • [36] B. Chen, 2013, soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci, 7 (1), 287-294.
  • [37] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, 1982, A note on semicontinuity and pre-continuity. Indian J. Pure Appl. Math. 13 (10), 1119-1123.
  • [38] S. Hussain, B. Ahmad, 2015, soft separation axioms in soft topological space submitted to elsvier.
  • [39] A. Kandil, O. A . E. Tantawy, S. A,EI Sheikh and A. M, Abd-e-Latif, 2014, soft semi separation axioms and some
  • [40] U. D. Tapi,Ranu Sharma,Bhagyashri A. Deole, 2014, Separation Axioms in Quad topological spaces, Bul Let in of Mathematical Science and Applications İS SN 2278-9634, Vol. 10, pp 16-18.
  • [41] N. F. Hameed and Yahya Abid, 2011,Certain types of separation axioms in Tritopological spaces,Iraqi Journal of science,Vol 52,No. 2,PP212-217.
  • [42] Y. Yumak and A. K. Kaymaci, 2015, some β-Open sets and their Applications, journal of New Theory, 4 (2015) 80-89.
There are 42 citations in total.

Details

Journal Section Research Article
Authors

Arif Mehmood Khattak

Asad Zaighum This is me

Muhammad Ishfaq This is me

Shamoona Jbeen This is me

Iqrar Hussain This is me

Publication Date December 24, 2017
Submission Date December 6, 2017
Published in Issue Year 2017 Issue: 19

Cite

APA Khattak, A. M., Zaighum, A., Ishfaq, M., Jbeen, S., et al. (2017). SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES. Journal of New Theory(19), 82-107.
AMA Khattak AM, Zaighum A, Ishfaq M, Jbeen S, Hussain I. SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES. JNT. November 2017;(19):82-107.
Chicago Khattak, Arif Mehmood, Asad Zaighum, Muhammad Ishfaq, Shamoona Jbeen, and Iqrar Hussain. “SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES”. Journal of New Theory, no. 19 (November 2017): 82-107.
EndNote Khattak AM, Zaighum A, Ishfaq M, Jbeen S, Hussain I (November 1, 2017) SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES. Journal of New Theory 19 82–107.
IEEE A. M. Khattak, A. Zaighum, M. Ishfaq, S. Jbeen, and I. Hussain, “SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES”, JNT, no. 19, pp. 82–107, November 2017.
ISNAD Khattak, Arif Mehmood et al. “SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES”. Journal of New Theory 19 (November 2017), 82-107.
JAMA Khattak AM, Zaighum A, Ishfaq M, Jbeen S, Hussain I. SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES. JNT. 2017;:82–107.
MLA Khattak, Arif Mehmood et al. “SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES”. Journal of New Theory, no. 19, 2017, pp. 82-107.
Vancouver Khattak AM, Zaighum A, Ishfaq M, Jbeen S, Hussain I. SOME CONTRIBUTION OF SOFT RUGULAR OPEN SETS TO SOFT SEPARATION AXIOMS IN SOFT QUAD TOPOLOGICAL SPACES. JNT. 2017(19):82-107.


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