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The further unified theory for modifications of λ-closed sets and gΛ-sets using minimal structures

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Abstract

We introduce and study two new notions of sets called (Λ, mn)-closed sets and gΛ mn -sets, which are defined on a nonempty set with two minimal structures. These sets enables us to unify modifications of λ-closed sets [1] and generalized Λ-sets [15], respectively. Moreover, we give a new characterization of the class of mn-T 1/2 [17] by using gΛ mn -sets.

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References

  1. Arenas, F.G., Dontchev, J., Ganster, M.: On λ-sets and dual of generalized continuity, Questions Answers Gen. Topology, 15 (1997), 3–13

    MATH  MathSciNet  Google Scholar 

  2. Caldas, M.: On Maps and Generalized Λ s -sets, East-West J. Math., 2 (2000), 181–190

    MATH  MathSciNet  Google Scholar 

  3. Caldas, M.: More on Generalized Homeomorphisms in Topological Spaces, Divulgaciones Matemáticas, 9 (2001), 55–63

    MATH  MathSciNet  Google Scholar 

  4. Caldas, M., Dontchev, J.: G.Λ s -sets and G.V s -sets, Mem. Fac. Sci. Kochi Univ. (Math.), 21 (2000), 21–30

    MATH  MathSciNet  Google Scholar 

  5. Caldas, M., Ganster, M., Georgiou, D.N., Jafari, S., Popa, V.: On generalization of closed sets, Kyungpook Math. J., 47 (2007), 155–164

    MATH  MathSciNet  Google Scholar 

  6. Caldas, M., Georgiou, D.N., Jafari, S.: Study of (Λ, α)-closed sets and the related notions in topological spaces, Bull. Malays. Math. Sci. Soc., 30 (2007), 23–36

    MATH  MathSciNet  Google Scholar 

  7. Caldas, M., Georgiou, D.N., Jafari, S., Noiri, T.: On (Λ, θ)-closed sets, Questions Answers Gen. Topology, 23 (2005), 69–87

    MATH  MathSciNet  Google Scholar 

  8. Caldas, M., Jafari, S.: On θ-semigeneralized closed sets in topology, Kyungpook Math J., 43 (2003), 135–148

    MATH  MathSciNet  Google Scholar 

  9. Cammaroto, F., Noiri, T.: On Λ m -sets and related topological spaces, Acta Math. Hungar., 109 (2005), 261–279

    Article  MATH  MathSciNet  Google Scholar 

  10. Dontchev, J., Maki, H.: On sg-closed sets and semi-λ-closed sets, Questions Answers Gen. Topology, 15 (1997), 259–266

    MATH  MathSciNet  Google Scholar 

  11. Ganster, M., Jafari, S., Noiri, T.: On pre-Λ-sets and pre-V-sets, Acta Math. Hungar., 95 (2002), 337–343

    Article  MATH  MathSciNet  Google Scholar 

  12. Georgiou, D.N., Jafari, S., Noiri, T.: Properties of (Λ, σ)-closed sets in topological spaces, (submitted)

  13. Levine, N.: Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41

    Article  MATH  MathSciNet  Google Scholar 

  14. Levine, N.: Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (1970), 89–96

    Article  MATH  MathSciNet  Google Scholar 

  15. Maki, H.: Generalized Λ-sets and the associated closure operator, The special Issue in commemoration of Prof. Kazuada IKEDA’s Retirement, (1986), 139–146

  16. Maki, H., Rao, K.C., Nagoor Gani A.: On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49 (1999), 17–29

    MathSciNet  Google Scholar 

  17. Noiri, T.: The further unified theory for modifications of g-closed sets, Rend. Circ. Mat. Palermo, 57 (2008), 411–421

    Article  MATH  MathSciNet  Google Scholar 

  18. Noiri, T., Popa, V.: A unified theory of closed functions, Bull. Math. Soc. Sci. Math. Roumanie, 49(97) (2006), 371–382

    MathSciNet  Google Scholar 

  19. Popa, V., Noiri, T.: On M-continuous functions, Anal. Univ. “Dunǎrea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., 18(23) (2000), 31–41

    Google Scholar 

  20. Popa, V., Noiri, T.: A unified theory of weak continuity for functions, Rend. Circ. Mat. Palermo (2), 51 (2002), 135–164.

    Google Scholar 

  21. Rosas, E., Carpintero, C., Sanabria, J.: (α, β)-Semi open sets and some new generalized separation axioms, Sci. Math. Jpn., 62 (2005), 397–403

    MATH  MathSciNet  Google Scholar 

  22. Sanabria, J., Rosas, E., Carpintero, C.: Una generalización de Λ s -conjuntos y V s -conjuntos mediante operadores asociados a una topología y funciones asociadas, Revista Colombiana de Matemáticas, 40 (2006), 87–103

    MathSciNet  Google Scholar 

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Correspondence to Ennis Rosas.

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Sanabria, J., Rosas, E. & Carpintero, C. The further unified theory for modifications of λ-closed sets and gΛ-sets using minimal structures. Rend. Circ. Mat. Palermo 58, 453–465 (2009). https://doi.org/10.1007/s12215-009-0035-x

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