Super and Strong γ H-Lindel¨ofness in Hereditary m-Spaces

Year 2024, Volume: 14 Issue: 2, 54 - 64, 31.07.2024

Ahmad Al-omari , Hanan Al-saadi , Takashi Noiri

Abstract

Let (X, m, H) be a hereditary m-space and γ : m → P(X) be a γ-operation
on m. A subset A of X is said to be γH-Lindel¨of relative to X [1] if for every cover
{Uα : α ∈ ∆} of A by m-open sets of X, there exists a countable subset ∆0 of ∆ such
that A \ ∪{γ(Uα) : α ∈ ∆0} ∈ H. In this paper, we define and investigate two kinds of
strong forms of “γ H-Lindel¨of relative to X”.

Keywords

hereditary m-space, γH-Lindel¨ofness, strong γH-Lindel¨ofness, super γH-Lindel¨ofness.

References

• [1] A. Al-Omari, T. Noiri, Generalizations of Lindelof spaces via a hereditary classes, Acta Univ. Sapientiae Math., 13(2), 2021, 281-291 .
• [2] H. Ogata, Operations on topological spaces and associated topology, Math. Japan., 36, 1991, 175-184.
• [3] V. Popa, T. Noiri, On M-continuous functions, An. Univ. ”Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., 43(23), 2000, 31–41.
• [4] T. Noiri, A unified theory for generalizations of compact spaces, Anal. Univ. Sci. Budapest., 54, 2011, 79–96.
• 5] S. Lugojan, Generalized topology, Stud. Cerc, Mat., 34, 1982, 348-360.
• [6] A. Cs´asz´ar, ´ Modification of generalized topologies via hereditary classes, Acta Math. Hungar., 115(1-2), 2007, 29-35.
• [7] A. Al-Omari, S. Modak, T. Noiri, On θ-modifications of generalized topologies via hereditary classes, Commun. Korean Math. Soc., 31(4), 2016, 857- 868.
• [8] A. Al-Omari, T. Noiri, Operators in minimal spaces with hereditary classes, Mathematica, 61(84)(2), 2019, 101-110.
• [9] A. Al-Omari, T. Noiri, Properties of γH-compact spaces with hereditary classes, Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali, 98(2), 2020, 1-11.
• [10] H. Maki, K.C. Rao, A. Nagoor Gani, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49, 1999, 17–29.
• [11] K. Kuratowski, Topology, I, Academic Press, New York, 1966.
• [12] R. Vaidyanathaswani, The localization theory in set-topology, Proc. Indian Acad. Sci., 20, 1945, 51–62.
• [13] D. Jankovi´c, T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4), 1990, 295–310.