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More properties of generalized open sets in generalized topological spaces

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Języki publikacji
EN
Abstrakty
EN
Sarsak [M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427] studied some properties of generalized open sets in generalized topological spaces (GTSs); the primary purpose of this article is to investigate more properties of generalized open sets in GTSs. We mainly study the behaviours of regular closed sets, semi-open sets, regular semi-open sets, preopen sets, and β -open sets in GTSs analogous to their behaviours in topological spaces.
Wydawca
Rocznik
Strony
404--415
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
  • Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
Bibliografia
  • [1] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41, DOI: http://doi.org/10.1080/00029890.1963.11990039.
  • [2] A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
  • [3] M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
  • [4] Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), no. 1–2, 53–66, DOI: http://doi.org/10.1007/s10474-005-0005-5.
  • [5] M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427, DOI: http://doi.org/10.1515/dema-2013-0453.
  • [6] M. S. Sarsak, More on μ-semi-Lindelöf sets in μ-spaces, Demonstr. Math. 54 (2021), no. 1, 259–271, DOI: https://doi.org/10.1515/dema-2021-0026.
  • [7] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351–357, DOI: http://doi.org/10.1023/A:1019713018007.
  • [8] Á. Császár, Extremally disconnected generalized topologies, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 47 (2004), 91–96.
  • [9] T. Noiri, Unified characterizations for modifications of R0 and R1 topological spaces, Rend. Circ. Mat. Palermo (2) 55 (2006), no. 1, 29–42, DOI: https://doi.org/10.1007/BF02874665.
  • [10] Á. Császár, Further remarks on the formula for gamma-interior, Acta Math. Hungar. 113 (2006), no. 4, 325–332, DOI: http://doi.org/10.1007/s10474-006-0109-6.
  • [11] Á. Császár, Remarks on quasi topologies, Acta Math. Hungar. 119 (2008), no. 1–2, 197–200, DOI: http://doi.org/10.1007/s10474-007-7023-4.
  • [12] D. Andrijević, Semi-preopen sets, Mat. Vesnik 38 (1986), no. 1, 24–32.
  • [13] Di Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math. 18 (1987), no. 3, 226–233.
  • [14] D. E. Cameron, Properties of S-closed spaces, Proc. Amer. Math. Soc. 72 (1978), 581–586.
  • [15] R. Engelking, General Topology, Sigma Series in Pure Mathematics, Second edition, vol. 6, Heldermann-Verlag, Berlin, 1989.
  • [16] M. S. Sarsak, Weakly μ-compact spaces, Demonstr. Math. 45 (2012), no. 4, 929–938, DOI: http://doi.org/10.1515/dema-2013-0411.
  • [17] M. S. Sarsak, On μ-compact sets in μ-spaces, Questions Answers Gen. Topol. 31 (2013), no. 1, 49–57.
  • [18] M. S. Sarsak, On semicompact sets and associated properties, Int. J. Math. Math. Sci. 2009 (2009), 465387, DOI: https://doi.org/10.1155/2009/465387.
  • [19] M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J. 27 (1987), no. 2, 135–143.
  • [20] M. S. Sarsak, SCP spaces, Questions Answers Gen. Topol. 28 (2010), no. 2, 187–195.
  • [21] B. Al-Nashef, On semipreopen sets, Questions Answers Gen. Topol. 19 (2001), no. 2, 203–212.
  • [22] A. S. Mashhour, I. A. Hasanein, and S. N. El-Deeb, A note on semicontinuity and precontinuity, Indian J. Pure Appl. Math. 13 (1982), no. 10, 1119–1123.
  • [23] T. Noiri, On semi-continuous mappings, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 54 (1973), no. 2, 210–214.
  • [24] K. Dlaska, rc-Lindelof sets and almost rc-Lindelof sets, Kyungpook Math. J. 34 (1994), no. 2, 275–281.
  • [25] C. Dorsett, Semiregularization spaces and the semi-closure operator, s-closed spaces and quasi-irresolute functions, Indian J. Pure Appl. Math. 21 (1990), no. 5, 416–422.
  • [26] M. S. Sarsak, On s-closed sets and rs-Lindelöf sets, Questions Answers Gen. Topol. 29 (2011), no. 2, 119–130.
Uwagi
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Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
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Bibliografia
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