Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON SOME NEW MAXIMAL AND MINIMAL SETS VIA θ-OPEN SETS

  • Caldas, Miguel (DEPARTAMENTO DE MATEMATICA APLICADA UNIVERSIDADE FEDERAL FLUMINENSE) ;
  • Jafari, Saeid (DEPARTMENT OF ECONOMICS UNIVERSITY OF COPENHAGEN) ;
  • Moshokoa, Seithuti P. (DEPARTMENT OF MATHEMATICS APPLIED MATHEMATICS AND ASTRONOMY)
  • Received : 2006.04.06
  • Published : 2010.10.31
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Abstract

Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal $\theta$-open sets, minimal $\theta$-closed sets, $\theta$-semi maximal open and $\theta$-semi minimal closed and investigate some of their fundamental properties.

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References

  1. F. Nakaoka and N. Oda, Some applications of minimal open sets, Int. J. Math. Math. Sci. 27 (2001), no. 8, 471–476. https://doi.org/10.1155/S0161171201006482
  2. F. Nakaoka and N. Oda, Some properties of maximal open sets, Int. J. Math. Math. Sci. (2003), no. 21, 1331–1340. https://doi.org/10.1155/S0161171203207262
  3. N. V. Velicko, H-closed topological spaces, Mat. Sb. (N.S.) 70(112) (1966), 98–112.