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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 2 | Year 2019 | Article Id. IJMTT-V65I2P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I2P501

On α−Irresolute Topological Rings


Madhu Ram, Shallu Sharma, Sahil Billawria, Tsering Landol
Abstract

We introduce the theory of α-irresolute topological rings. We present some examples of α-irresolute topological rings and discuss their relationship with topological rings. Some basic properties of α-irresolute topological rings are investigated. It is proved that every α-irresolute topological ring is α-regular.

Keywords
α-open sets, α-irresolute mappings, α-irresolute topological rings.
References

[1] V.I.Arnautov, M.I. Vodinchar and A.V. Mikhalev, Introduction to the Theory of Topological Rings and Modules (Shtiinca, Kishinev, 1981) (in Russian).
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[5] I.Kaplansky, Topological rings, Bull. Amer. Math. Soc., 54 (1948), 809-826.
[6] A.Kar and P. Bhattacharyya, Bitopological α−compact spaces, Riv. Mat. Univ. Parma, 1(7) (2002), 159-176.
[7] N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly. 70(1963), 36-41.
[8] S.N.Maheshwari and S.S. Thakur, α−irresolute mappings, Tamkang J. Math., 11 (1980), 209-214.
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[10] S.Warner, Topological Rings, North Holland, 1993.
[11] H.M.M.Salih, On Irresolute Topological Rings, J. Adv. Stud. Topol., 9(2) (2018), 130-134.
[12] M.Shalini and M. Sathyavathy, Solving Graphically Sine Wave Second Order Boundary Value Problem using Laplace Transform and Finite Difference Method, International Journal of Mathematics Trends and Technology , 65 (1) (2019), 57-61.


Citation :

Madhu Ram, Shallu Sharma, Sahil Billawria, Tsering Landol, "On α−Irresolute Topological Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 2, pp. 1-5, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I2P501

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