Characteristics of Soft Tychonoff Spaces with New Soft Separation Axioms

Authors

  • Shuker Mahmood Department of Mathematics, College of Science, University of Basrah, Iraq

DOI:

https://doi.org/10.31185/eduj.Vol2.Iss25.2745

Keywords:

Characteristics

Abstract

The aim of this work is to investigate and study soft Tychonoff space and some new soft spaces such as soft , soft , soft , soft , soft , soft , soft and soft in this work the relationships between these new soft spaces such as soft public regular, soft public normal, soft strongly completely regular, soft semi completely normal and with well known axioms soft , soft and soft are obtained, Further, the relationships between these new soft spaces with each other are studied. We prove that each soft space is soft Tychonoff space, also in this paper we show that each soft space is soft , each soft space is soft and each soft space is soft . Finally, depending on the above soft spaces and properties of the soft fuzzy spaces, the new types of soft fuzzy spaces can be introduced like Soft fuzzy public regular, Soft fuzzy strongly completely regular, and others.

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References

P. K. Maji, A. R. Roy and R. Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001), 589–602.

C. Janaki and D. Sreeja, On Soft πgb-Continuous Functions in Soft Topological Spaces, International Journal of Mathematics Trends and Technology, 10(1) (2014), 1-11.

S. Hussain and B. Ahmad, Some properties of soft topological spaces, Computers & Mathematics with Applications, 62(11), (2011) 4058–4067.

A. Saha and A. Mukherjee, Soft interval-valued intuitionistic fuzzy rough sets, Annals of Fuzzy Mathematics and Informatics, 9( 2) ( 2015), 279–292.

C. Yang, A not on soft set theory, Computers and Mathematics with Applications, 56 (2008), 1899–1900.

S. Roy and T. K. Samanta, A note on fuzzy soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2) (2012), 305- 311.

I. Zorlutuna, M. Akdag, K. W. Min, and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Math. and Info., 3(2) (2012), 171-185.

F. Feng, Y. B. Jun, and X. Zhao, Soft semirings, Computers and Mathematics with Applications, 56 (10) (2008), 2621-2628.

P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Comput. Math. Appl., 45 (2003), 555-562.

H. Aktas, N. Cagman, Soft sets and soft groups, Information Sciences, 1 (77) (2007) 2726-2735.

M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications 57(2009) 1547-1553.

S. Mahmood, Soft Regular Generalized b-Closed Sets in Soft Topological Spaces, Journal of Linear and Topological Algebra, Vol. 03, No. 04, 2014, 195- 204.

article_510050_4ac0956f45f51114ac59f26782eb7c83.pdf

S. Mahmood, On intuitionistic fuzzy soft b-closed sets in intuitionistic fuzzy soft topological spaces, Annals of Fuzzy Mathematics and Informatics, Volume 10, No. 2, pp. 221-233 (2015). afmi.or.kr -SM KHALIL

S. Mahmood and Z. Al-Batat, Intuitionistic Fuzzy Soft LA- Semigroups and Intuitionistic Fuzzy Soft Ideals, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 6 ( 2016), 119 – 132. MAHMOOD & AL-BATAT.pdf - Open eClass

S. Mahmood, Dissimilarity Fuzzy Soft Points and their Applications, Fuzzy Information and Engineering, 8(2016), 281-294. http://dx.doi.org/10.1016/j.fiae.2016.11.003

S. Mahmood, Soft Sequentially Absolutely Closed Spaces, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 7 (2017), 73-92.

P.K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.

D. A. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(1999)19-31.

 [19] W. K. Min, A note on soft topological spaces, Computers and Mathematics with Applications 62 (2011) 3524-3528.

A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 7(2), (2014) 181-196.

A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, Soft semi separation axioms and some types of soft functions, Annals of Fuzzy Mathematics and Informatics, 8(2), (2014) 305-318.

M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786-1799.

P. K. Maji, R. Biswas, and A. R. Roy, Fuzzy soft set, J. Fuzzy Math. 9(3), 677-692 (2001)

D. Molodtsov, V.Y. Leonov and D.V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1(1) (2006), 8–39.

A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural computing and Applications, 21(1)(2012), 113-119.

V. Banu and H. Aygun, Soft sets over power sets: Generalities and applications to topology, Journal of intelligent and Fuzzy systems, 29(1) (2015),389-395.

M. Akdag and A. Ozkan, Soft b-open sets and soft b-continuous functions, Math Sci (2014) 8:124.

O. Tantawy, S. A. El-Sheikh and S. Hamde, Separation axioms on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 11(4) (2016), 511-525.

A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Fuzzy Soft Semi Connected Properties in Fuzzy Soft Topological Spaces, Math. Sci. Lett. 4, No. 2, (2015), 171-179.

B.P. Varol, H. Aygun, Fuzzy soft topology, Hacet. J. Math. Stat. 41(3) (2012), 407–419.

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Published

2021-12-05

How to Cite

Shuker Mahmood. (2021). Characteristics of Soft Tychonoff Spaces with New Soft Separation Axioms. Journal of College of Education, 2(25), 1423-1446. https://doi.org/10.31185/eduj.Vol2.Iss25.2745