On $\alpha^{*}-$continuous and contra $\alpha^{*}-$continuous mappings in topological spaces with soft setting

Document Type : Research Paper


1 Ministry of Education, Directorate General of Education/ Baghdad/ Al-Kark/3, Iraq.

2 Department of Mathematics, College of Science, University of Basrah, Basrah 61004, Iraq.

3 Ministry of Education, The General Directorate For Al-Najaf Al Ashraf, Iraq


In this work, some new connotations of continuous mappings such as $\alpha^{*}$ - continuous mapping $\left(\alpha^{*}-C M\right),$ irresolute $\alpha^{*}-$mapping $\left(I \alpha^{*}-C M\right),$ and strongly $\alpha^{*}-$ continuous mapping $\left(S \alpha^{*}-C M\right)$ are studied and some of their characteristics are discussed. In other side, new some classes of contra continuous mappings are investigated in this work, they are called contra $\alpha^{*}$ - continuous mapping $\left(C \alpha^{*}-C M\right)$.


[1] O. Njstad, On some classes of nearly open sets, Pacific J. Math.15(3) (1965) 961-970.
[2] N.M. Abbas, On some types of weakly open sets, MSC. Thesis, Baghdad University, 2004.
[3] G.B. Navalagi =, Definition Bank in general topology, Topology Atlas, 2002.
[4] H.A. Othman, New types of α-continuous mapping, Thesis, Mustansiriya University, 2004)
[5] N.M. Ali and S.M. Khalil, On α∗- open sets in topological spaces, IOP Conf. Ser.: Mater. Sci. Engin. 571(2019) 012021.
[6] J. Dontchev, Survey on preopen sets, Proc. Yatsushiro Topological Conf., 1998, pp. 1-8.
[7] A.R. Nivetha, M. Vigneshwaran, N.M. Ali Abbas and S.M. Khalil, On N∗gα-continuous in topological spaces of neutrosophy, J. Interdiscip. Math. 24(3) (2021) 677-685
[8] S.M. Khalil and F. Hameed, An algorithm for the generating permutation algebras using soft spaces, J. Taibah Univ, Sci. 12(3) (2018) 299-308.
[9] S.M. Khalil and M.H. Hasab, Decision making using new distances of intuitionistic fuzzy sets and study their application in the universities, INFUS, Adv. Intel. Syst. Comput. 1197 (2020) 390-396.
[10] S.M. Khalil and A. Rajah, Solving the class equation xd = β in an alternating group for each β ∈ H ∩ Cα and n∉θ, J. Assoc. Arab Univer. Basic and Appl. Sci. 10 (2011), 42-50.
[11] S.M. Khalil and A. Rajah, Solving class equation xd = β in an alternating group for all n ∈ θ and β ∈ Hn ∩ Cα, J. Assoc. Arab Univer. Basic and Appl. Sci. 16 (2014) 38-45.
[12] S.M. Khalil, Enoch Suleiman and Modhar M. Torki, Generated New Classes of Permutation I/B-Algebras, Journal of Discrete Mathematical Sciences and Cryptography, (2021), to appear
[13] S.M. Khalil, The permutation topological spaces and their bases, Basrah J. Sci. A 32(1) (2014) 28-42.
[14] S.M. Khalil and N.M.A. Abbas, On nano with their applications in medical field, AIP Conf. Proc., 2020, 2290, 040002.
[15] S.M. Khalil, New category of the fuzzy d-algebras, J. Taibah Univ. Sci.12(2) (2018) 143-149.
[16] N.M. Ali Abbas, S.M. Khalil and M. Vigneshwaran, The neutrosophic strongly open maps in neutrosophic bitopological spaces, J. Interdiscip. Math. 24(3) (2021) 667-675.
[17] K. Damodharan, M. Vigneshwaran and S.M. Khalil, Nδ ∗ gα -continuous and irresolute functions in neutrosophic topological spaces, Neutrosophic Sets Syst. 38(1) (2020) 439-452.
[18] M.M. Torki and S.M. Khalil, New types of finite groups and generated algorithm to determine the integer factorization by excel, AIP Conf. Proc. 2290 (2020) 040020.
[19] S.M. Khalil and N.M. Abbas, Applications on new category of the symmetric groups, AIP Conf. Proc. 2290 (2020) 040004.
[20] S.M. Khalil and F. Hameed, Applications on Cyclic Soft Symmetric Groups, IOP Conf. Ser.: J. Phys.1530 (2020) 012046.
[21] S.M. Saied and S.M. Khalil, Gamma Ideal Extension in Gamma Systems, J. Discrete Math. Sci. Cryptography (2021), to appear.
[22] S.M. Khalil, Dissimilarity fuzzy soft points and their applications, Fuzzy Inf. Engin. 8(3) (2016) 281-294.
[23] S.M. Khalil and F. Hameed, Applications of fuzzy-Ideals in-algebras, Soft Comput. 24(18) (2020) 13997- 14004.
[24] S.A. Abdul-Ghani, S.M. Khalil, M. Abd Ulrazaq and A.F. Al-Musawi, New branch of intuitionistic fuzzification in algebras with their applications, Int. J. Math. Math. Sci. 2018 (2018) Article ID 5712676, 6 pages.
[25] S.M. Khalil, Decision making using algebraic operations on soft effect matrix as new category of similarity measures and study their application in medical diagnosis problems, J. Intel. Fuzzy Syst. 37 (2019) 1865-1877.
[26] S.M. Khalil and S.A. Abdul-Ghani, Soft M-ideals and soft S-ideals in soft S-algebras, IOP Conf. Series: J. Phys. 1234 (2019) 012100.
[27] S.M. Khalil and F. Hameed, An algorithm for generating permutations in symmetric groups using soft spaces with general study and basic properties of permutations spaces, J. Theory Appl. Inf. Technol. 96(9) (2018) 2445-2457.
[28] S.M. Khalil, M. Ulrazaq, S. Abdul-Ghani and A.F. Al-Musawi, σ-algebra and σ-Baire in fuzzy soft setting, Adv. Fuzzy Syst. 2018 (2018), Article ID 5731682, 10 pages.
[29] M.A. Hasan, S.M. Khalil, and N.M.A. Abbas, Characteristics of the soft-(1, 2)-gprw closed sets in soft bi-topological spaces, Conference IT-ELA 2020, 9253110, 2020, pp. 103–108.
[30] S.M. Khalil and A. Hassan, Applications of fuzzy soft ρ-ideals in ρ -algebras, Fuzzy Inf. Engin. 10(4) (2018) 467-475.
[31] S.M. Khalil, Decision making using new category of similarity measures and study their applications in medical diagnosis problems, Afr. Mat. (2021). DOi-10.1007/s13370-020-00866-2
[32] N.M. Ali Abbas and S.M. Khalil, On new classes of neutrosophic continuous and contra mappings in neutrosophic topological spaces, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 719-725.
[33] M.A. Hasan, N.M. Ali Abbas and S.M. Khalil, On soft α∗-open sets and soft contra α∗-continuous mappings in soft topological spaces, J. Interdiscip. Math. 24(3) (2021) 729-734.
[34] R. Stam, The algebra of bounded continuous functions into a non-Archimedean field, Pacific J. Math. 50 (1974) 169-185.
[35] A. Kharal and B. Ahmad, Mappings on soft classes, New Math. Nat. Comput. 7(3) (2011) 471481.
[36] M. Shabir and M. Naz, On Soft topological spaces, Comp. And Math. Appl. 61(7) (2011) 1786-1799.
Volume 12, Issue 1
May 2021
Pages 1107-1113
  • Receive Date: 05 September 2021
  • Revise Date: 03 March 2021
  • Accept Date: 14 March 2021