Some independent results on Ideal-Rothberger spaces
https://doi.org/10.22405/2226-8383-2026-27-1-134-138
Abstract
In this article we show that in a regular 𝑝-space, for every pair of disjoint ideal Rothberger set and closed set there is a pair of disjoint open sets such that one contains the closed set and other one’s complement with respect to the ideal rothberger set is in the corresponding sub ideal. Moreover, we demonstrate how families of closed sets can be used to describe the ideal Rothberger spaces.
About the Author
Bal Prasenjit
The Institute of Chartered Financial Analysts of India University Tripura
India
India
Ph.D. in Mathematics
References
1. Bal, P. 2023, “A countable intersection like characterization of star-Lindel¨of spaces”, Researches in Mathematics, vol. 31, no. 2, pp. 3–7.
2. Bal, P. & Bhowmik, S. 2017, “On R-star-Lindel¨of spaces”, Palestine Journal of Mathematics, vol. 6, no. 2, pp. 480–486.
3. Bal, P., Bhowmik, S. & Gauld, D. 2018, “On selectively star-Lindel¨of properties”, Journal of the Indian Mathematical Society, vol. 85, no. 3-4, pp. 291–304.
4. Bal, P. & Koˇcinac, L.D.R. 2020, “On selectively star-ccc spaces”, Topology and its Applications, vol. 281, art. id. 107181, doi: 10.1016/j.topol.2020.107181.
5. Bal, P. & De, R. 2023, “On strongly star semi-compactness of topological spaces”, Khayyam Journal of Mathematics, vol. 9, no. 1, pp. 54–60.
6. Bal, P. 2023, “On the class of I-𝛾-open cover and I-St-𝛾-open cover”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 3, pp. 630–639.
7. Bhardwaj, M. 2018, “Addendum to ’Ideal Rothberger spaces” ’, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 69–75.
8. Engelking, R. 1989, General topology, Sigma Series in Pure Mathematics, Revised and complete edn, Heldermann Verlag, Berlin.
9. Gillman, L. & Henriksen, M. 1954, “Concerning rings of continuous functions”, Transactions of the American Mathematical Society, vol. 77, no. 2, pp. 340–362.
10. G¨uld¨urdek, A. 2018, “Ideal Rothberger spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 69–75.
11. G¨uld¨urdek, A. 2023, “More on ideal Rothberger spaces”, European Journal of Pure and Applied Mathematics, vol. 16, no. 1, pp. 1–4.
12. Newcomb, R.L. 1967, “Topologies which are compact modulo an ideal”, PhD thesis, University of California at Santa Barbara.
Review
For citations:
Prasenjit B. Some independent results on Ideal-Rothberger spaces. Chebyshevskii Sbornik. 2026;27(1):134-138. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-1-134-138
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