Volume 68 | Issue 7 | Year 2022 | Article Id. IJMTT-V68I7P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I7P505
Received | Revised | Accepted | Published |
---|---|---|---|
30 May 2022 | 04 Jul 2022 | 10 Jul 2022 | 19 Jul 2022 |
In this paper, we introduce a new class of open sets is called ๐๐ -open set . Also, we present the notion of ๐๐ - continuous, ๐๐ -open, ๐๐ -irresolute, ๐๐ -totally continuous, and ๐๐ -contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some ๐๐ - separation axioms and the mappings are related with ยฏ๐๐ -separation axioms.
[1] S. Mashhour, I. A. Hasanein, and S. N. El-Deeb, โฮฑ-Continuous and ฮฑ-Open Mappings,โ Acta Math.Hungar, vol. 41, no. 3-4, pp. 213โ218, 1983.
[2] Arhangel. Skii A. V, Ludwig L, โOn ฮฑ-Normal and ฮฒ-Normal Spaces,โ Comment. Math Univ. Carolinae, vol. 42, no. 3, pp. 507- 519, 2001.
[3] E. Ekici and M. Caldas, โSlightlyโContinuous Functions,โ Bol. Soc. Para Mat., vol. 22, no. 2, pp. 63 โ 7, 2004.
[4] J. Donchev, โContra Continuous Functions and Strongly S-Closed Spaces,โ Internat. J. Math. Math. Sci., vol. 19, pp. 303-310, 1996.
[5] J. Donchev and T. Noiri, โContra Semi Continuous Functions,โ Math. Panonica., vol. 10, no. 2, pp. 154-168, 1999.
[6] N. Biswas, โSome Mappings in Topological Spaces,โ Bull. Cal. Math. Soc., vol. 61, pp. 127โ133, 1969.
[7] N. Levine, โSemi-Open Sets and Semi-Continuity in Topological Spaces,โ Amer. Math. Monthly, vol. 70, pp. 36-41, 1963.
[8] O. Njastad, โOn Some Classes of Nearly Open Sets,โ Pacific J. Math, vol. 15, pp. 961-970, 1965.
[9] R. L. Ellis, โA Non-Archimedean Analogue of the Tietze-Urysohn Extension Theorem,โ Nederl. Akad.Wetensch. Proc. Ser.A, vol. 70, pp. 332-333, 1967.
[10] R. Staum, โThe Algebra of Bounded Continuous Functions into a Non-Archimedean Field,โ Pacific J. Math., vol. 50, pp. 169-185, 1974.
[11] S. G. Crossley and S. K, โHildebrand Semi-Topological Properties Fund,โ Math, vol. 74, pp. 233-254, 1972.
[12] S. Jafari and T. Noiri, โContra-ฮฑ-Continuous Functions Between Topological Spaces,โ Iranian Int. J. Sci., vol. 2, pp. 153-167, 2001.
[13] S. N. Maheshwari and R. Prasad, โOn s-Normal Spaces,โ Bull. Math. Soc. Sci. Math. R. S. Roumanie (N. S.), vol. 22, no. 68, pp. 27- 29, 1978.
[14] S. N. Maheswari and S. S. Thakur, โOn ฮฑ-Irresolute Mappings,โ Tamkang J. Math, vol. 11, pp. 209-214, 1980.
[15] S. W. Askander, M.Sc. Thesis, โThe Property of Extended and Non-Extended Topological for Semi-Open, ฮฑ-Open and i-Open Sets with Application,โ College of Education, University of Mosul, 2011.
[16] T. Noiri, โSuper Continuity and Some Strong Forms of Continuity,โ Indian J. Pure Appl. Math, vol. 15, no. 3, pp. 241โ250, 1984.
[17] Y. Beceren, โOn Semi ฮฑ-Irresolute Functions,โ J. Indian. Acad. Math, vol. 22, pp. 353-362, 2000.
[18] Amir A. Mohammed Omar Y. Khattab, โOn iฮฑ - Open Sets,โ Raf. J. of Comp. & Mathโs., vol. 9, no. 2, pp. 219-228, 2012.
[19] Omar Y. Khattab, M.S.c Thesis, โOn iฮฑ-Open Sets in Topological Spaces and Their Application,โ College of Education, University of Mosul, 2013.
[20] Tadoros, S. F, "ON ฮฑ-Homeomorphism of Topological Space", AinShama Sci. Bull, vol. 28A, pp. 81-98, 1990
Omar y. khattab, "Upper semi-Advanced Mappings in a Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 7, pp. 26-33, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I7P505