Two notes on ``On soft Hausdorff spaces"
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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\"{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.
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\"{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.
참고문헌 (8)
- M. I. Ali, "On some new operations in soft set theory", Comput. Math. Appl, 57, pp.1547~1553 (2009)
- A. Aygunoglu, "Some notes on soft topological spaces", Neural Comput. & Applic, 21, pp.113~119 (2012)
- S. Das, "Soft metric", Ann. Fuzzy Math. Inform, 6(1), pp.77~94 (2013)
- D. Molodtsov, "Soft set theory-first results", Comput. Math. Appl, 37, pp.19~31 (1999)
- S. Nazmul, "Neighbourhood properties of soft topological spaces", Ann. Fuzzy Math. Inform, 6(1), pp.1~15 (2013)
- M. Shabir, "On soft topological spaces", Comput. Math. Appl, 61, pp.1786~1799 (2011)
- B. P. Varol, "On soft Hausdorff spaces", Ann. Fuzzy Math. Inform, 5(1), pp.15~24 (2013)
- I. Zorlutuna, "Remarks on soft topological spaces", Ann. Fuzzy Math. Inform, 3(2), pp.171~185 (2012)