Generalized closed sets in hereditary m-spaces with gamma-operations
Resumo
abstract: Let (X,m, H) be a hereditary m-space and : m -----> P(X) be an operation on m. In this paper,
a subset A of X is said to be H g-closed if Cl(A) \ U in H whenever A \ U and U is m-open. We obtain
some characterizations and properties of H g-closed and H g-open sets.
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Referências
A. Al-Omari and T. Noiri, On Ψ∗-operator in ideal m-spaces, Bol. Soc. Paran. Mat. (3s.), 30 (1)(2012), 53 – 66.
A. Al-Omari and T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math., 43(2) (2013), 139-149.
A. Al-Omari and T. Noiri, On operators in ideal minimal spaces, Mathematica, 58(81), No. 1-2 (2016), 3– 13.
A. Al-Omari and T. Noiri, A note on topologies generated by m-structures and ω-topologies, Commun. Fac. Sci. Univ. Ank. Series A1, 67 (1) (2018), 141–146.
A. Al-Omari and T. Noiri, Properties of γH-compact spaces with hereditary classes, Atti Accad. Pelor. Peric., Cl. Sci. Fis. Mat. Natur. 98 (2) (2020), A4 [11 pages].
A. Al-Omari and T. Noiri, Operators in minimal spaces with hereditary classes, Mathematica, 61(84), No. 2 (2019), 101– 110.
A. Al-Omari and T. Noiri, Generalizations of Lindel¨of spaces via hereditary classes, Acta Univ. Sapientie Math. 13 (2) (2021), 281-291.
A. Al-Omari and T. Noiri, Properties of θ-H-compact sets in hereditary m-spaces, Acta Et Commentationes Universitatis Tartuensis De Mathematica 26 (2) (2022), 193-206.
F. Cammaroto and T. Noiri, On Λm-sets and related topological spaces, Acta Math. Hungar., 109(3) (2005), 261–279.
A. Csaszar, Modification of generalized topologies via hereditary classes, Acta Math. Hungar., 115(1-2) (2007), 29-35.
A. Csaszar, γ-connected sets, Acta Math. Hungar, 101(4), (2003), 273–279, https://doi.org/10.1023/B:AMHU.0000004939.57085.9e
D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4) (1990), 295–310.
K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo (2), 19 (1970), 89-96.
H. Maki, K. C. Rao and A. Nagoor Gani, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49 (1999), 17–29.
S. Modak, Dense sets in weak structure and minimal structure, Commun. Korean Math. Soc., 28(3), (2013), 589–596. https://doi.org/10.4134/CKMS.2013.28.3.589
S. Modak and T. Noiri, Some generalizations of locally closed sets,, Iran. J. Math. Sci. Inform., 14(1), (2019), 159–165. DOI: https://doi.org/10.7508/ijmsi.2019.01.014
S. Modak and T. Noiri, Connectedness of ideal topological spaces, Filomat, 29(4), (2015), 661–665.
S. Modak and S. Selim, Set operators and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 70(1), (2021), 456–467, doi: 10.31801/cfsuasmas.644689.
T. Noiri, A unified theory for modifications of g-closed sets, Rend. Circ. Mat. Palermo 56 (2007), 171-184.
T. Noiri, A unified theory for generalizations of compact spaces, Anal. Univ. Sci. Budapest., 54 (2011), 79–96.
H. Ogata, Operations on topological spaces and associated topology, Math. Japon. 36(1) (1991), 175-184.
V. Popa and T. Noiri, On M-continuous functions, An. Univ. ”Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor. (2), 43(23) (2000), 31–41.
R. Vaidyanathaswani, The localization theory in set-topology, Proc. Indian Acad. Sci., 20 (1945), 51–62.
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