A note on α−irresolute topological rings

Madhu Ram


In [4], we introduced the notion of α−irresolute topological rings in Mathematics. This notion is independent of topological rings. In this note, we point out that under certain conditions an α−irresolute topological ring is topological ring and vice versa. We prove that the Minkowski sum A+B of an α−compact subset A ⊆ R and an α−closed subset B ⊆ R of an α−irresolute topological ring (R, =) is actually a closed subset of R. In the twilight of this note, we pose several questions which are worthy


α−open sets, α−closed sets, α−irresolute topological rings.

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D. Jangkovic, I.J. Reilly and M. K. Vamanamurthy, On strongly compact topological spaces, Question and answer in General Topology, 6(1) (1988), 29-40.

N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.

O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.

M. Ram, S. Sharma, S. Billawria and T. Landol, On α−irresolute topological rings, International Journal of Mathematics Trends and Technology, 65 (2) (2019)

DOI: http://dx.doi.org/10.23755/rm.v38i0.523


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