Some properties and mappings on weakly \(\nu \)-Lindelöf generalized topological spaces

Volume 10, Issue 8, pp 4150--4161 http://dx.doi.org/10.22436/jnsa.010.08.11

Publication Date: August 10, 2017 Submission Date: April 05, 2017

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Authors

M. Abuage - Institute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia. A. Kılıçman - Department of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia.

Abstract

Our work aims to study weakly \(\nu \)-Lindelöf (briefly \(w\nu \)-Lindelöf) space in generalized topological spaces. Some characterizations of \(w\nu \)-Lindelöf subspaces and subsets are showed. Furthermore, we shall show that the \(w\nu \)-Lindelöf generalized topological space is not a hereditary property. Finally, the effect of some mappings and decompositions of continuity are studied. The main result that we obtained on is the effect of almost \((\nu, \mu)\)-continuous function on \(w\nu \)-Lindelöf generalized topological space.

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Keywords

• \(\nu \)-Lindelöf
• \(w\nu \)-Lindelöf
• \(G\)-semiregular generalized topological space.

MSC

•  54A05
•  54B05
•  54C05
•  54C10
•  54D15
•  54D20

References

• [1] M. Abuage, A. Kılıçman, Some Properties and Decomposition on \(a\nu \)-Lindelöf generalized topological spaces, , (submitted),


• [2] M. Abuage, A. Kılıçman, M. S. Sarsak, Generalization of soft \(\nu \)-compact soft generalized topological spaces, arXiv, 2016 (2016), 10 pages.
  • Google Scholar


• [3] M. Abuage, A. Kılıçman, M. S. Sarsak, \(n\nu \)-Lindelöfness, Malay. J. Math. Sci., 11 (2017), 73–86.
  • MathSciNet


• [4] A. Al-omari, T. Noiri, A unified theory of contra-(\(\nu,\lambda\))-continuous functions in generalized topological spaces, Acta Math. Hungar., 135 (2012), 31–41.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] M. Arar , A note on spaces with a countable \(\nu \)-base, Acta Math. Hungar., 144 (2014), 494–498.
  • View Article
  • MathSciNet
  • MATH


• [6] J. B. T. Ayawan, J. S. R. Canoy , Axioms of Countability in Generalized Topological Spaces, Int. Math. Forum, 8 (2013), 1523–1530.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] F. Cammaroto, G. Santoro, Some counterexamples and properties on generalizations of Lindelöf spaces, Internat. J. Math. Math. Sci., 19 (1996), 737–746.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65–87.
  • View Article
  • Google Scholar


• [9] Á. Császár , Generalized topology, generalized continuity , Acta Math. Hungar., 96 (2002), 351–357.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] Á. Császár, Extremally disconneted genealized topologies, Annales Univ. Sci. Budapest Sectio Math., 47 (2004), 91–96.


• [11] Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), 53–66.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] Á. Császár , Further remarks on the formula of \(\gamma\)-interior, Acta Math. Hungar., 113 (2006), 325–332.
  • View Article
  • Google Scholar
  • MATH


• [13] Á. Császár, \(\delta\)-and \(\theta\)-modifications of generalized topologies, Acta Math. Hungar., 120 (2008), 275–279.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] E. Ekici, Generalized submaximal spaces, Acta Math. Hungar., 134 (2011), 132–138.
  • View Article
  • MathSciNet
  • Google Scholar


• [15] A. J. Fawakhreh, A. Kılıçman, On generalizations of regular-Lindelöf spaces , Internat. J. Math. and Math. Sci., 27 (2001), 535–539.
  • View Article
  • MathSciNet
  • Google Scholar


• [16] A. Kılıçman, M. Abuage, On some spaces generated by \(\nu\)-regular sets, JP J. Geom. Topol., 18 (2015), 15–35.
  • View Article
  • MathSciNet


• [17] A. S. Mashhour, M. A. El-Monsef, I. A. Hasanein, T. Noiri, Strongly compact spaces, Delta J. Sci., 8 (1984), 30–46.
  • Google Scholar


• [18] W. K. Min, Almost continuity on generalized topological spaces, Acta Math. Hungar., 125 (2009), 121–125.
  • View Article
  • MathSciNet
  • Google Scholar


• [19] W. K. Min, (\(\delta,\delta'\))-continuity on generalized topological spaces, Acta Math. Hungar., 129 (2010), 350–356.
  • View Article
  • Google Scholar
  • MATH


• [20] W. K. Min, Y.-K. Kim , Some strong forms of \((g, g')\)-continuity on generalized topological spaces , Honam Math. J., 33 (2011), 85–91.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] T. Noriri , Unified characterizations for modifications of \(R_0\) and \(R_1\) topological spaces, Rend. Circ. Mat. Palermo, 55 (2006), 29–42.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] T. Noiri, V. Popa , The unified theory of certain types of generalizations of Lindelöf spaces , Demonstratio Math., 43 (2010), 203–212.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] Z. Salleh, A. Kılıçman, Pairwise almost Lindelöf bitopological spaces, Malaysian J. of Math. Sci., 1 (2007), 227–238.
  • Google Scholar


• [24] Z. Salleh, A. Kılıçman, On pairwise nearly Lindelöf bitopological spaces , Far East J. of Math. Sci., 77 (2013), 147–171.
  • Google Scholar
  • MATH


• [25] Z. Salleh, A. Kılıçman, On pairwise weakly Lindelöf bitopological spaces, Bulletin of the Iranian Math. Society, 39 (2013), 469–486.
  • MathSciNet
  • Google Scholar
  • MATH


• [26] M. S. Sarsak , On some properties of generalized open sets in generalized topological spaces, Demonstratio Math., 46 (2013), 415–427.
  • View Article
  • MathSciNet
  • Google Scholar


• [27] M. S. Sarsak, , On \(\nu\)-compact sets in \(\mu\)-spaces, Questions Answers in Gen. Topology, 31 (2013), 49–57.