Volume 25 • Issue 4 • PP: 26-41 • 2025
SoftWeak θ-Continuity and Preservations of Soft Hyperconnectedness and Soft Near Compactness
View PDF Abstract
In this paper, we introduce a new weak form of soft continuity called soft weak θ-continuity in soft topological spaces and investigate the relationships between soft weak θ-continuity and θ-continuity (resp. soft weak continuity and soft δ-continuity). We obtain several characterizations of soft weak θ-continuity. Also, we give sufficient conditions for the equivalence between soft weak θ-continuity and soft θ-continuity (resp. soft δ-continuity). Moreover, we investigate the link between soft weak θ-continuity and weak θ-continuity in classical topology. Furthermore, via soft weak θ-continuity, we obtain preservation theorems of soft hyperconnectedness and soft near compactness. Finally, we obtain soft restriction, soft product, and soft graph theorems of soft weak θ-continuity.
Keywords
References
[1] Molodtsov, D. Soft set theory—first results. Global optimization, control, and games, III, Comput. Math. Appl. 1999; 37:19–31.
[2] Maji PK, Biswas R, Roy AR. Soft set theory. Comput. Math. Appl. 2003; 45:55–562.
[3] Kharal A, Ahmad B. Mappings of soft classes. New Math. Nat. Comput. 2011; 7:471–481.
[4] Molodtsov D, Leonov VY, Kovkov DV. Soft sets technique and its application. Nechetkie Sistemy i Myagkie Vychisleniya 2006; 1:8–39.
[5] Maji PK, Roy AR, Biswas R. An application of soft sets in a decision making problem. Comput. Math. Appl. 2002; 44:1077–1083.
[6] Shabir M, Naz M. On soft topological spaces. Comput. Math. Appl. 2011; 61:1786–1799.
[7] Majumdar P, Samanta SK. On soft mappings. Comput. Math. Appl. 2010; 60:2666–2672.
[8] Kharal A, Ahmad B. Mappings on soft classes. New Math. Nat. Comput. 2011; 7:471–481.
[9] Aygunoglu A, Aygun H. Some notes on soft topological spaces. Neural Comput. Appl. 2012; 21:113– 119.
[10] Georgiou DN, Megaritis AC, Petropoulos VI. On soft topological spaces. Appl. Math. Inform. Sci. 2013; 7:1889–1901.
[11] Sayed OR, Hassan N, Khalil AM. A decomposition of soft continuity in soft topological spaces. Afr. Mat. 2017; 28:887–898.
[12] Abuzaid D., Al-Ghour S. Soft strong θ-continuity and soft almost strong θ-continuity. AIMS Mathematics 2024; 9:16687–16703.
[13] Al Ghour S, Bin-Saadon A. On some generated soft topological spaces and soft homogeneity. Heliyon 2019; 5:e02061.
[14] Fomin S. Extensions of topological spaces. Ann. Math. 1943; 44:471–480.
[15] Levine N. A decomposition of continuity in topological spaces. The American Mathematical Monthly 1961; 68:44–46.
[16] Commaroto F, Noiri T. On weakly θ-continuous functions. Matematicki Vesnik 1986; 38:33–44.
[17] Jeyashri S, Tharmar S, Ramkumar G. On soft δ-continuous functions. Int. J. Math. Trends Tech.2017; 45, 28–34.
[18] Demir I, Ozbakır OB. Soft Hausdorff spaces and their some properties. Ann. Fuzzy Math. Inform. 2014; 8:769–783.
[19] Ramkumar S, Subbiah V. Soft separation axioms and soft product of soft topological spaces. Maltepe J. Math. 2020; 2:61–75.
[20] Kandil A. Soft connectedness via soft ideals. J. N. Results Sci. 2014; 4:90–108.
[21] Asaad BA. Results on soft extremally disconnectedness of soft topological spaces. Journal of Mathematics and Computer Science 2017; 17:448–464.
[22] Yuksel S, Tozlu N, Ergul ZG. Soft regular generalized closed sets in soft topological spaces. Int. J. Math. Anal. 2014; 8:355–367.
[23] Mohammed RA, Sayed OR, Eliow A. Some properties of soft delta-topology. Acad. J. Nawroz Univ. 2019; 8:352–361.
[24] Debnath B. A note on soft nearly compact and soft nearly paracompactness in soft topological spaces. Int. J. Innov. Res. Sci. Eng. Technol. 2017; 6:15906–15914.
[25] Hosny RA, Abd El-Latif AM. Soft G-compactness in soft topological spaces. Annals of Fuzzy Mathematics and Informatics 2016; 11:973–987.
Cite This Article
Choose your preferred format