Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MORE ON MAXIMAL, MINIMAL OPEN AND CLOSED SETS

  • Received : 2015.12.16
  • Published : 2017.01.31
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Abstract

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

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References

  1. P. Howard and E. Tachtsis, On the minimal cover property in ZF, Topology Appl. 173 (2014), 94-106. https://doi.org/10.1016/j.topol.2014.05.021
  2. A. Mukharjee, On maximal, minimal open and closed sets, Commun. Korean Math. Soc. 30 (2015), no. 3, 277-282 https://doi.org/10.4134/CKMS.2015.30.3.277
  3. 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
  4. F. Nakaoka and N. Oda, Some properties of maximal open sets, Int. J. Math. Math. Sci. 21 (2003), no. 21, 1331-1340.
  5. F. Nakaoka and N. Oda, Minimal closed sets and maximal closed sets, Int. J. Math. Math. Sci. 2006 (2006), Article ID 18647, 8 pages.
  6. L. A. Steen and J. A. Seebach Jr., Counterexamples in topology, New York: Holt, Rinehart and Winston Inc., 1970.