Research Article
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Soft β-Separation Axioms in Soft Quad Topological Spaces

Year 2018, Issue: 22, 22 - 38, 26.03.2018

Arif Mehmood Khattak Fahad Jamal Zaheer Anjum Younas Khan İshfaq Ahmed

Abstract

The major purpose of this article is to publicize soft β-separations
axioms in soft quad topological spaces. We talk over and focus our attention on
soft β-separation axioms in soft quad topological spaces with respect to
ordinary points and soft points. Moreover study the inherited characteristics
at different respects with respect to ordinary points and soft points. Some of
their `principal properties in soft quad topological spaces are also brought
under consideration.

Keywords

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

References

  • [1] B. M. Ittanagi, Soft bi-topological spaces , international journal of computer application (0975 8887), v107- No. 7. December 2014.
  • [2] S. A El-Sheikh, Rodyna A. Hosny and A.M Abd-e-Latif, Characterization of b soft separation Axioms in soft topological spaces in Inf. Sci. Lett.4 (3) (2015) 125-133.
  • [3] M. Naz, M. Shabir and M. I. Ali, Separation axiom in bi soft topological spaces , Arxiv. 1850 of .00866 vl [Math, GN] 29 August 2015.
  • [4] D. A Molodtsov, Soft set theory first results, Comp. Math. Appl., 37, (1999), 19-31.
  • [5] J. C Kelly, Bitopological spaces proc London math-soc, 13(1963), 71-81.
  • [6] P. K Maji, R, Biswas and A. R. Roy, Soft set theory, Comp. Math. Appl., 45, (2003), 555-562.
  • [7] M. Shabir and M.Naz, on soft topological space, Comp. Math. Appl., 61(2011) 1786-1799.
  • [8] M.Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operation in soft set theory.Comp.Math.Appl. 57, (2009), 1547-1553.
  • [9] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci 1(77) (2007) 2726-2735.
  • [10] Chen, The paramatrization reduction of soft sets and application, Comp. Math, Appl., 49(2005)757-763.
  • [11] F. Feng, Y. B. Jun, X. Z. Zhao, Soft semi rings, Comp. Math. Appl., 56 (2008) 2621-2628
  • [12] Z. Kong, L. Gao, L. Wang , S. Li, The normal parameter reduction of soft set and its algorithm. Comp., Math. Appl., 56(2008)3029-3027.
  • [13] Y. B. Jun, C.H. Park, Application of soft sets and ideal theory of BCK/BCI-algebra, Inf, Sci 178(2008)2466-2475.
  • [14] Pie and D. Miao, 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, 2005,pp.617-621.
  • [15] Majumdar and S. K. Samanta, on soft mapping, Comp. Math. Appl., 60(2010)2666-2672.
  • [16] B. Jun, Soft BSK/BCI-algebra, Comp. Math. Appl., 56(2008)1408-1413.
  • [17] Shabir and M. I. Ali, Soft ideals and generalized fuzzy ideals in semi-groups, New Math. Wat. Comp. 5(2009)599-615
  • [18] Y. Zou and Z. Xiao, Data analysis approach of soft sets under incomplete information, Knowledge-Based System, 21 (2008) 941-945.
  • [19] A. Aygunoglu and H. Aygun, Some notes on soft topological space, Neural Comp and Applic DoI 10.1007/s.00521-011-0722-3.
  • [20] H. B. Ahmad, Some properties of soft topological spaces ,Comp. Math. App., 62 (2011) 4058-4067.
  • [22] D. N. Geogiou, A. C. Megartis, V.I. Petropounlos: On soft topological spaces , Appl, Math. Inf, Sci 7 (2) (2013) 1889-190
  • [23] B. Chen, Soft semi open sets and related properties in soft topological spaces . Appl, math, Inf, sci 7(1), 287-294(2013).
  • [24] A. Kandil , O. A. E. Tantawy , S.A,EI Sheikh and A.M , Abd-e- Latif , operation and decomposition of some form of soft continuity of soft topological spaces via soft ideal, Ann Fuzzy Math , inf , 9 (3)(2015)385-402.
  • [25] A. Kandil, O. A. E. Tantawy, S.A, EI Sheikh and A.M, Abd-e- Latif, Soft connectedness via soft ideal, Journal of New result in science, 4 (2014)90-108.
  • 26] A. Kandil, O. A. E. Tantawy, S. A. EI Sheikh and A. M. Abd-e-Latif, Soft ideal theory, soft local function and generalize soft topological spaces , Appl. Math. Inf. Sci, 8(4) (2014)1595-1603.
  • [27] A. Kandil. O. A. E. Tantawy , S. A. EI Sheikh and A. M. Abd-e- Latif, Soft regularity and normality based on semi open soft sets and soft ideals,App. Math. Inf. Sci. Lett, 3(2015)47-55.
  • [28] A. Kandil, O. A. E. Tantawy, S. A. EI Sheikh and A. M. Abd-e-Latif, Soft semi compactness, via soft ideals, Appl. Math. Inf. Sci, 8(5) (2014)2297-2306
  • [29] A. Kandil , O. A. E. Tantawy , S. A. EI Sheikh and A. M. Abd-e-Latif, Soft semi (Quasi) husdorff spaces via soft ideals, South Asian , J.Math, 4(6)(2014)265-284.
  • [30] I.Zorlutana,N.Akdog ,W.K.Min, S.Atmaca:Remarks on soft Topological spaces , Annals , of Fuzzy Mathematics and informatics 3(2)(2012)171-185
  • [31] J. Mahanta, P. K. Das, On soft Topological spaces Via semi open and semi closed soft sets ,ar XIV:1203.1433VI[math,G.N]16Mar 2012.
  • [32] A. Kandil, O. A. E. Tantawy, S. A. El -Sheikh and A. M Abd- Latif , Sopra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces Appl. Math. Inf. Sci , (4)(2014) 1731- 1740.
  • [33] S. A. El- Sheikh and A.M Abd-e-Latif, Decomposition of some type of supra soft sets and soft continuity, international journal of mathematics trends and technology, 9 (1) (2014) 37-56.
  • [34] L. A. Zadeh: Fuzzy sets, information and control 8(1965) 338-353.
  • [35] 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.
  • [36] C. H. Park, Y. B. Jun, M. A. Ozturk, Soft W.S-Algebras , Communications of the Korean Mathematical Society 23(3)(2008) 313- 324.
  • [37] I. Arockiarani and A. A. Lancy, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces , IJMRS, 4(2), (2013) 1-7.
  • [38] B. Chen, Soft semi-open sets and related properties in soft topological spaces . Appl. Math. Inf. Sci, 7(1) (2013) 287-294.
  • [39] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On pre continuous and weak pre-continuous mapings. Proc. Math. Phys. Soc. Egypt 53 (1982) 47-53.
  • [40] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, A note on semi-continuity and pre-continuity. Indian J. Pure Appl. Math. 13(10) (1982) 1119- 1123.
  • [41] T. Noiri, A. S. Mashhour and S. N. El-Deeb, on p-regular spaces. Bull. Math. Soc. Sci. Math. R. S. Roumaine 27(75) (1983) 437-441.
  • [42] Y. G. nanambal, On Generalized Pre-regular Closed Sets in topological Spaces. Indian J. Pure. Appl. Math., 28(3) (1997) 351-360.
  • [43] J. Dontchev, I. Arokiarani and K. Balachandran, Some characterizations of gp-irresolute and gp-continuous maps between topological spaces . Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 20(1999) 93-104.
  • [44] E. Ekici, Almost contra pre-continuous function. Bull Malays Math. Sci. Soc. 27(1) (2004) 53-65.
  • [45] J. Dontchev and H. Maki, On behavior of gp- closed sets and their generalization. Mem. Fac. Sci. Kochi Univ. Math., 19 (1998) 57-72.
  • [46] V. M. K. R. S. Kumar, Semi-pre-generalized closed sets. Mem Fac. Sci. Kochi Univ. Ser. A. Math., 20 (1999) 33-46.
  • [47] S. Jafari and T. Noiri, On contra-pre-continuous functions. Bull Malaysian Math. Soc. 25(2) (2002) 115-28.
  • [48] T. Noiri, H. Maki and J. Umehara, Generalized pre-closed functions. Mem Fac. Sci. Kochi Univ. Ser. A, Math. 19 (1998) 13-20.
  • [49] L. Arokia and Arokiarani, On soft β-separation axioms. IJMRS, Vol. 1 Issue 5, October-2013.
  • [50] Z. Kong. L. Gao .L.Wang, S.Li: The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications 56 (2008), 3029-3037.
  • [51] S. Hussain, B. Ahmad, Soft separation axioms in soft topological space submitted to elsvier 28 September 2015.
  • [52] A. Kandil, O. A. E. Tantawy, S. A, EI Sheikh and A. M. Abd-e-Latif, Soft semi separation axioms and some types of soft functions, Annals of fuzzy mathematics and informatics, 8(2) (2014) 305-318.
  • [53] U.D.Tapi, Ranu Sharma, Bhagyashri A. Deole, Separation Axioms in Quad Topological Spaces , Bulletin of Mathematical Science and Applications ISSN: 2278-9634, Vol.10, pp 16-18. 2014.
  • [54] N. F. Hameed and Yahya Abid, Certain types of separation axioms in Tri-topological spaces ,Iraqi Journal of Science,Vol 52, No.2, 2011, PP212-217.

Year 2018, Issue: 22, 22 - 38, 26.03.2018

Arif Mehmood Khattak Fahad Jamal Zaheer Anjum Younas Khan İshfaq Ahmed

Abstract

References

  • [1] B. M. Ittanagi, Soft bi-topological spaces , international journal of computer application (0975 8887), v107- No. 7. December 2014.
  • [2] S. A El-Sheikh, Rodyna A. Hosny and A.M Abd-e-Latif, Characterization of b soft separation Axioms in soft topological spaces in Inf. Sci. Lett.4 (3) (2015) 125-133.
  • [3] M. Naz, M. Shabir and M. I. Ali, Separation axiom in bi soft topological spaces , Arxiv. 1850 of .00866 vl [Math, GN] 29 August 2015.
  • [4] D. A Molodtsov, Soft set theory first results, Comp. Math. Appl., 37, (1999), 19-31.
  • [5] J. C Kelly, Bitopological spaces proc London math-soc, 13(1963), 71-81.
  • [6] P. K Maji, R, Biswas and A. R. Roy, Soft set theory, Comp. Math. Appl., 45, (2003), 555-562.
  • [7] M. Shabir and M.Naz, on soft topological space, Comp. Math. Appl., 61(2011) 1786-1799.
  • [8] M.Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operation in soft set theory.Comp.Math.Appl. 57, (2009), 1547-1553.
  • [9] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci 1(77) (2007) 2726-2735.
  • [10] Chen, The paramatrization reduction of soft sets and application, Comp. Math, Appl., 49(2005)757-763.
  • [11] F. Feng, Y. B. Jun, X. Z. Zhao, Soft semi rings, Comp. Math. Appl., 56 (2008) 2621-2628
  • [12] Z. Kong, L. Gao, L. Wang , S. Li, The normal parameter reduction of soft set and its algorithm. Comp., Math. Appl., 56(2008)3029-3027.
  • [13] Y. B. Jun, C.H. Park, Application of soft sets and ideal theory of BCK/BCI-algebra, Inf, Sci 178(2008)2466-2475.
  • [14] Pie and D. Miao, 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, 2005,pp.617-621.
  • [15] Majumdar and S. K. Samanta, on soft mapping, Comp. Math. Appl., 60(2010)2666-2672.
  • [16] B. Jun, Soft BSK/BCI-algebra, Comp. Math. Appl., 56(2008)1408-1413.
  • [17] Shabir and M. I. Ali, Soft ideals and generalized fuzzy ideals in semi-groups, New Math. Wat. Comp. 5(2009)599-615
  • [18] Y. Zou and Z. Xiao, Data analysis approach of soft sets under incomplete information, Knowledge-Based System, 21 (2008) 941-945.
  • [19] A. Aygunoglu and H. Aygun, Some notes on soft topological space, Neural Comp and Applic DoI 10.1007/s.00521-011-0722-3.
  • [20] H. B. Ahmad, Some properties of soft topological spaces ,Comp. Math. App., 62 (2011) 4058-4067.
  • [22] D. N. Geogiou, A. C. Megartis, V.I. Petropounlos: On soft topological spaces , Appl, Math. Inf, Sci 7 (2) (2013) 1889-190
  • [23] B. Chen, Soft semi open sets and related properties in soft topological spaces . Appl, math, Inf, sci 7(1), 287-294(2013).
  • [24] A. Kandil , O. A. E. Tantawy , S.A,EI Sheikh and A.M , Abd-e- Latif , operation and decomposition of some form of soft continuity of soft topological spaces via soft ideal, Ann Fuzzy Math , inf , 9 (3)(2015)385-402.
  • [25] A. Kandil, O. A. E. Tantawy, S.A, EI Sheikh and A.M, Abd-e- Latif, Soft connectedness via soft ideal, Journal of New result in science, 4 (2014)90-108.
  • 26] A. Kandil, O. A. E. Tantawy, S. A. EI Sheikh and A. M. Abd-e-Latif, Soft ideal theory, soft local function and generalize soft topological spaces , Appl. Math. Inf. Sci, 8(4) (2014)1595-1603.
  • [27] A. Kandil. O. A. E. Tantawy , S. A. EI Sheikh and A. M. Abd-e- Latif, Soft regularity and normality based on semi open soft sets and soft ideals,App. Math. Inf. Sci. Lett, 3(2015)47-55.
  • [28] A. Kandil, O. A. E. Tantawy, S. A. EI Sheikh and A. M. Abd-e-Latif, Soft semi compactness, via soft ideals, Appl. Math. Inf. Sci, 8(5) (2014)2297-2306
  • [29] A. Kandil , O. A. E. Tantawy , S. A. EI Sheikh and A. M. Abd-e-Latif, Soft semi (Quasi) husdorff spaces via soft ideals, South Asian , J.Math, 4(6)(2014)265-284.
  • [30] I.Zorlutana,N.Akdog ,W.K.Min, S.Atmaca:Remarks on soft Topological spaces , Annals , of Fuzzy Mathematics and informatics 3(2)(2012)171-185
  • [31] J. Mahanta, P. K. Das, On soft Topological spaces Via semi open and semi closed soft sets ,ar XIV:1203.1433VI[math,G.N]16Mar 2012.
  • [32] A. Kandil, O. A. E. Tantawy, S. A. El -Sheikh and A. M Abd- Latif , Sopra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces Appl. Math. Inf. Sci , (4)(2014) 1731- 1740.
  • [33] S. A. El- Sheikh and A.M Abd-e-Latif, Decomposition of some type of supra soft sets and soft continuity, international journal of mathematics trends and technology, 9 (1) (2014) 37-56.
  • [34] L. A. Zadeh: Fuzzy sets, information and control 8(1965) 338-353.
  • [35] 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.
  • [36] C. H. Park, Y. B. Jun, M. A. Ozturk, Soft W.S-Algebras , Communications of the Korean Mathematical Society 23(3)(2008) 313- 324.
  • [37] I. Arockiarani and A. A. Lancy, Generalized soft gβ-closed sets and soft gsβ-closed sets in soft topological spaces , IJMRS, 4(2), (2013) 1-7.
  • [38] B. Chen, Soft semi-open sets and related properties in soft topological spaces . Appl. Math. Inf. Sci, 7(1) (2013) 287-294.
  • [39] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On pre continuous and weak pre-continuous mapings. Proc. Math. Phys. Soc. Egypt 53 (1982) 47-53.
  • [40] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, A note on semi-continuity and pre-continuity. Indian J. Pure Appl. Math. 13(10) (1982) 1119- 1123.
  • [41] T. Noiri, A. S. Mashhour and S. N. El-Deeb, on p-regular spaces. Bull. Math. Soc. Sci. Math. R. S. Roumaine 27(75) (1983) 437-441.
  • [42] Y. G. nanambal, On Generalized Pre-regular Closed Sets in topological Spaces. Indian J. Pure. Appl. Math., 28(3) (1997) 351-360.
  • [43] J. Dontchev, I. Arokiarani and K. Balachandran, Some characterizations of gp-irresolute and gp-continuous maps between topological spaces . Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 20(1999) 93-104.
  • [44] E. Ekici, Almost contra pre-continuous function. Bull Malays Math. Sci. Soc. 27(1) (2004) 53-65.
  • [45] J. Dontchev and H. Maki, On behavior of gp- closed sets and their generalization. Mem. Fac. Sci. Kochi Univ. Math., 19 (1998) 57-72.
  • [46] V. M. K. R. S. Kumar, Semi-pre-generalized closed sets. Mem Fac. Sci. Kochi Univ. Ser. A. Math., 20 (1999) 33-46.
  • [47] S. Jafari and T. Noiri, On contra-pre-continuous functions. Bull Malaysian Math. Soc. 25(2) (2002) 115-28.
  • [48] T. Noiri, H. Maki and J. Umehara, Generalized pre-closed functions. Mem Fac. Sci. Kochi Univ. Ser. A, Math. 19 (1998) 13-20.
  • [49] L. Arokia and Arokiarani, On soft β-separation axioms. IJMRS, Vol. 1 Issue 5, October-2013.
  • [50] Z. Kong. L. Gao .L.Wang, S.Li: The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications 56 (2008), 3029-3037.
  • [51] S. Hussain, B. Ahmad, Soft separation axioms in soft topological space submitted to elsvier 28 September 2015.
  • [52] A. Kandil, O. A. E. Tantawy, S. A, EI Sheikh and A. M. Abd-e-Latif, Soft semi separation axioms and some types of soft functions, Annals of fuzzy mathematics and informatics, 8(2) (2014) 305-318.
  • [53] U.D.Tapi, Ranu Sharma, Bhagyashri A. Deole, Separation Axioms in Quad Topological Spaces , Bulletin of Mathematical Science and Applications ISSN: 2278-9634, Vol.10, pp 16-18. 2014.
  • [54] N. F. Hameed and Yahya Abid, Certain types of separation axioms in Tri-topological spaces ,Iraqi Journal of Science,Vol 52, No.2, 2011, PP212-217.
There are 53 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Arif Mehmood Khattak

Fahad Jamal This is me

Zaheer Anjum This is me

Younas Khan This is me

İshfaq Ahmed This is me

Publication Date March 26, 2018
Submission Date December 26, 2017
Published in Issue Year 2018 Issue: 22

Cite

APA Khattak, A. M., Jamal, F., Anjum, Z., Khan, Y., et al. (2018). Soft β-Separation Axioms in Soft Quad Topological Spaces. Journal of New Theory(22), 22-38.
AMA Khattak AM, Jamal F, Anjum Z, Khan Y, Ahmed İ. Soft β-Separation Axioms in Soft Quad Topological Spaces. JNT. March 2018;(22):22-38.
Chicago Khattak, Arif Mehmood, Fahad Jamal, Zaheer Anjum, Younas Khan, and İshfaq Ahmed. “Soft Β-Separation Axioms in Soft Quad Topological Spaces”. Journal of New Theory, no. 22 (March 2018): 22-38.
EndNote Khattak AM, Jamal F, Anjum Z, Khan Y, Ahmed İ (March 1, 2018) Soft β-Separation Axioms in Soft Quad Topological Spaces. Journal of New Theory 22 22–38.
IEEE A. M. Khattak, F. Jamal, Z. Anjum, Y. Khan, and İ. Ahmed, “Soft β-Separation Axioms in Soft Quad Topological Spaces”, JNT, no. 22, pp. 22–38, March 2018.
ISNAD Khattak, Arif Mehmood et al. “Soft Β-Separation Axioms in Soft Quad Topological Spaces”. Journal of New Theory 22 (March 2018), 22-38.
JAMA Khattak AM, Jamal F, Anjum Z, Khan Y, Ahmed İ. Soft β-Separation Axioms in Soft Quad Topological Spaces. JNT. 2018;:22–38.
MLA Khattak, Arif Mehmood et al. “Soft Β-Separation Axioms in Soft Quad Topological Spaces”. Journal of New Theory, no. 22, 2018, pp. 22-38.
Vancouver Khattak AM, Jamal F, Anjum Z, Khan Y, Ahmed İ. Soft β-Separation Axioms in Soft Quad Topological Spaces. JNT. 2018(22):22-38.


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