Communications of the Korean Mathematical Society (대한수학회논문집)

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

  • Received : 2015.04.24
  • Published : 2015.06.30
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Abstract

We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

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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 (2003), no. 21, 1331-1340. https://doi.org/10.1155/S0161171203207262
  3. F. Nakaoka and N. Oda, Minimal closed sets and maximal closed sets, Int. J. Math. Math. Sci. 2006 (2006), Article ID 18647, pages 1-8.
  4. S. Willard, General Topology, Addison-Wesley Publishing Company, 1970.

Cited by

  1. On Mean Open and Closed Sets vol.56, pp.4, 2016, https://doi.org/10.5666/KMJ.2016.56.4.1259