• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.697-705
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• 2023

We studied new notions of analogues of topological rings. Salih [10] acquaints us with the notion of irresolute topological ring in 2018. In this paper, we further studied the space closely and characterized indispensable properties of the space. We prove that every open subset of an irresolute topological ring is irresolute topological ring. We also obtained the equivalent condition of neighborhood of an element in an irresolute topological ring. It is proved that ring homeomorphism of an irresolute topological ring is irresolute if it is irresolute at identity element e in the irresolute topological ring 𝓡.