Annals of Fuzzy Mathematics and Informatics

The Natural Science Institute Wonkwang University (원광대학교 기초자연과학연구소)
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Two notes on "On soft Hausdorff spaces"

  • El-Shafei, M.E. (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Abo-Elhamayel, M. (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Al-shami, T.M. (Department of Mathematics, Faculty of Science, Sana'a University)
  • Received : 2018.05.27
  • Accepted : 2018.08.03
  • Published : 2018.12.25
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Abstract

One of the well known results in general topology says that every compact subset of a Hausdorff space is closed. This result in soft topology is not true in general as demonstrated throughout this note. We begin this investigation by showing that [Theorem 3.34, p.p.23] which proposed by Varol and $Ayg{\ddot{u}}n$ [7] is invalid in general, by giving a counterexample. Then we derive under what condition this result can be generalized in soft topology. Finally, we evidence that [Example 3.22, p.p. 20] which introduced in [7] is false, and we make a correction for this example to satisfy a condition of soft Hausdorffness.

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References

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Cited by

  1. Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone vol.24, pp.7, 2018, https://doi.org/10.1007/s00500-019-04295-7
  2. Sum of Soft Topological Spaces vol.8, pp.6, 2018, https://doi.org/10.3390/math8060990
  3. Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem vol.39, pp.3, 2020, https://doi.org/10.1007/s40314-020-01161-3
  4. Comments on some results related to soft separation axioms vol.31, pp.7, 2018, https://doi.org/10.1007/s13370-020-00783-4
  5. Compactness on Soft Topological Ordered Spaces and Its Application on the Information System vol.2021, pp.None, 2021, https://doi.org/10.1155/2021/6699092
  6. Methodological remarks on soft topology vol.25, pp.5, 2018, https://doi.org/10.1007/s00500-021-05587-7