A note on α−irresolute topological rings

Authors

  • Madhu Ram Department of Mathematics, University of Jammu. Jammu-180006, India

DOI:

https://doi.org/10.23755/rm.v38i0.523

Keywords:

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

Abstract

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

References

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)

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Published

2020-06-30

Issue

Vol. 38 (2020)

Section

Volume 38-2020

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