Some Alternative Interpretations of Strongly Star Semi-Rothberger and Related Spaces

Sarkar, Susmita; Bal, Prasenjit

doi:10.2478/tmmp-2024-0003

Abstract

In this article, some under-appreciated characteristics of strongly star-Rothberger subsets are explored. Additionally, with the aid of the SSI property and MSSI property, semi-Rothberger and star semi-Rothberger spaces are represented by families of closed sets. Finally, several selection principle like attributes are produced that can reflect the previously mentioned sequential covering features in an inverted form.

References

BAL, P.—DE, R.: On strongly star semi-compactness of topological spaces, Khayyam J. Math. 9 (2023), no. 1, 54–60.
Search in Google Scholar Back to article
BAL, P.: On the class of I-γ-open cover and -St-γ-open cover, Hacet. J. Math. Stat. 52 (2023), no. 3, 630–639.
Search in Google Scholar Back to article
BAL, P.—SARKAR, S.: On strongly star g-compactness of topological spaces, Tatra Mt. Math. Publ. 85 (2023), 89–100.
Search in Google Scholar Back to article
BAL, P.—RAKSHIT, D.: A Variation of the Class of Statistical γ-Covers, Topol. Algebra Appl. 11 (2023), no. 1, 20230101, 9 pp.
Search in Google Scholar Back to article
BAL, P.—BHOWMIK, S.: On R-Star-Lindelöf Spaces, Palest. J. Math. 6 (2017), no. 2, 480–486.
Search in Google Scholar Back to article
BAL, P.—BHOWMIK, S.: Some new star-selection principles in topology, Filomat. 31 (2017), no. 13, 4041–4050.
Search in Google Scholar Back to article
BAL, P.—BHOWMIK, S.—GAULD, D.: On selectively Star-Lindelöf properties, J.Indian Math. Soc. (N.S.) 85 (2018), no. 3–4, 291–304.
Search in Google Scholar Back to article
BAL, P.—KOČINAC, L. D. R.: On selectively Star-ccc spaces, Topology Appl. 281 (2020), 107184, 8 pp.
Search in Google Scholar Back to article
BHARDWAJ, M.: Addendum to “semi-Rothberger and related spaces”, Bull. Iranian Math. Soc. 47 (2021), 959–960.
Search in Google Scholar Back to article
CROSSLEY, S. G.—HILDEBRAND, S. K.: Semi-closure, Texas J. Sci. 22 (1971), 99–112.
Search in Google Scholar Back to article
DOUWEN, E. K. V.—REED, G. M.—ROSCOE A. W.—TREE I. J.: Star covering properties, Topology Appl. 39 (1991), no. 1, 71–103.
Search in Google Scholar Back to article
KANDEMIR, H.S.—ET, M.—ARAL, N.D.: Strongly λ-convergence of order α in neutrosophic normed spaces, Dera Natung Government College Research Journal, 7, (2022), no. 1, 1—9. https://doi.org/10.56405/dngcrj.2022.07.01.01.
Search in Google Scholar Back to article
ENGELKING, R.: General Topology. In: Sigma Series in Pure Mathematics Vol. 6, (Revised and complete edition). Heldermann Verlag, Berlin, 1989.
Search in Google Scholar Back to article
KOČINAC L.D.R.: Star selection principles : A survey, Khayyam J. Math, 1 (2015), 82–106.
Search in Google Scholar Back to article
KOČINAC L. D. R.—SABHA, A.—KHAN, M. U.: Covering properties defined by semi-open sets, J.NonlinearSci.Appl. 9 (2016), 4388–4398.
Search in Google Scholar Back to article
KUMAR, G.—TYAGI B. K.: Remarks on semi-Menger and star semi-Menger spaces, Tatra Mt. Math. Publ. 81 (2022), 57–68.
Search in Google Scholar Back to article
LEVINE, N.: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.
Search in Google Scholar Back to article
MENGER, K.: EinigeÜberdeckungss¨atze der Punktmengenlehre, Sitzungsberichte. Math. Astronomie, Physik, Meteorologie und Mechanik, 133 (1924), 421–444.
Search in Google Scholar Back to article
SABHA, A.—KHAN, M.: Semi-Rothberger and related spaces, Bull. Iranian Math. Soc. 43 (2017), 1969–1987.
Search in Google Scholar Back to article
SCHEEPERS, M.: Combinatorics of open covers, Topology Appl. 69 (1996), 31–62.
Search in Google Scholar Back to article
SINGH, S.: Remarks on set-Menger and related properties, Topology Appl. 280 (2020), 107278, 4 pp.
Search in Google Scholar Back to article
SONG, Y. K.: Remarks on star-Hurewicz spaces, Bull. Polish Acad. Sci. Math. 61 (2013), 247–255.
Search in Google Scholar Back to article
YAYING, T.: Arithmetic continuity in cone metric space, Dera Natung Government College Research J. 5 (2020), no. 1, 55—62. https://doi.org/10.56405/dngcrj.2020.05.01.07.
Search in Google Scholar Back to article

Some Alternative Interpretations of Strongly Star Semi-Rothberger and Related Spaces

Abstract

Paradigm

My account