...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 7 | Year 2022 | Article Id. IJMTT-V68I7P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I7P505

Upper semi-Advanced Mappings in a Topological Spaces


Omar y. khattab
Received Revised Accepted Published
30 May 2022 04 Jul 2022 10 Jul 2022 19 Jul 2022
Abstract

In this paper, we introduce a new class of open sets is called ๐‘–๐‘ -open set . Also, we present the notion of ๐‘–๐‘ - continuous, ๐‘–๐‘ -open, ๐‘–๐‘ -irresolute, ๐‘–๐‘ -totally continuous, and ๐‘–๐‘ -contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some ๐‘–๐‘ - separation axioms and the mappings are related with ยฏ๐‘–๐‘ -separation axioms.

Keywords
๐‘–๐‘ -open set, ๐‘–๐‘ -continuous, ๐‘–๐‘ -open mapping, ๐‘–๐‘ -irresolute, ๐‘–๐‘ -totally continuous, ๐‘–๐‘ -contra-continuous
References

[1] S. Mashhour, I. A. Hasanein, and S. N. El-Deeb, โ€œฮฑ-Continuous and ฮฑ-Open Mappings,โ€ Acta Math.Hungar, vol. 41, no. 3-4, pp. 213โ€“218, 1983.
[2] Arhangel. Skii A. V, Ludwig L, โ€œOn 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, โ€œSlightlyโ€“Continuous Functions,โ€ Bol. Soc. Para Mat., vol. 22, no. 2, pp. 63 โ€“ 7, 2004.
[4] J. Donchev, โ€œContra 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, โ€œContra Semi Continuous Functions,โ€ Math. Panonica., vol. 10, no. 2, pp. 154-168, 1999.
[6] N. Biswas, โ€œSome Mappings in Topological Spaces,โ€ Bull. Cal. Math. Soc., vol. 61, pp. 127โ€“133, 1969.
[7] N. Levine, โ€œSemi-Open Sets and Semi-Continuity in Topological Spaces,โ€ Amer. Math. Monthly, vol. 70, pp. 36-41, 1963.
[8] O. Njastad, โ€œOn Some Classes of Nearly Open Sets,โ€ Pacific J. Math, vol. 15, pp. 961-970, 1965.
[9] R. L. Ellis, โ€œA 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, โ€œThe 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, โ€œHildebrand Semi-Topological Properties Fund,โ€ Math, vol. 74, pp. 233-254, 1972.
[12] S. Jafari and T. Noiri, โ€œContra-ฮฑ-Continuous Functions Between Topological Spaces,โ€ Iranian Int. J. Sci., vol. 2, pp. 153-167, 2001.
[13] S. N. Maheshwari and R. Prasad, โ€œOn 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, โ€œOn ฮฑ-Irresolute Mappings,โ€ Tamkang J. Math, vol. 11, pp. 209-214, 1980.
[15] S. W. Askander, M.Sc. Thesis, โ€œThe 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, โ€œSuper Continuity and Some Strong Forms of Continuity,โ€ Indian J. Pure Appl. Math, vol. 15, no. 3, pp. 241โ€“250, 1984.
[17] Y. Beceren, โ€œOn Semi ฮฑ-Irresolute Functions,โ€ J. Indian. Acad. Math, vol. 22, pp. 353-362, 2000.
[18] Amir A. Mohammed Omar Y. Khattab, โ€œOn iฮฑ - Open Sets,โ€ Raf. J. of Comp. & Mathโ€™s., vol. 9, no. 2, pp. 219-228, 2012.
[19] Omar Y. Khattab, M.S.c Thesis, โ€œOn 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

Citation :

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

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright ยฉ 2025 Seventh Sense Research Groupยฎ . All Rights Reserved