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Letter to the EditorComment on (Soft 𝛼-Open Sets and Soft𝛼-Continuous Functions)
Ahmed Mostafa Khalil
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
Correspondence should be addressed to Ahmed Mostafa Khalil; [email protected]
Received 15 October 2015; Accepted 4 November 2015
Academic Editor: Angelo Favini
Copyright © 2015 Ahmed Mostafa Khalil. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
Akdag and Ozkan pointed out in [1, Example 14] thatthe collection 𝜏 of soft sets is a soft topology over theuniverse 𝑋 = {𝑥
1, 𝑥2, 𝑥3, 𝑥4}, where 𝐸 = {𝑒
1, 𝑒2, 𝑒3} is
the set of parameters. This conclusion is not correct since(𝐹1, 𝐸) ∩̃ (𝐹
2, 𝐸) ∉ 𝜏, (𝐹
1, 𝐸) ∪̃ (𝐹
2, 𝐸) ∉ 𝜏, (𝐹
1, 𝐸) ∩̃ (𝐹
11,
𝐸) ∉ 𝜏, (𝐹1, 𝐸) ∩̃ (𝐹
14, 𝐸) ∉ 𝜏, (𝐹
1, 𝐸) ∪̃ (𝐹
14, 𝐸) ∉ 𝜏, (𝐹
2,
𝐸) ∪̃ (𝐹5, 𝐸) ∉ 𝜏, (𝐹
2, 𝐸) ∪̃ (𝐹
6, 𝐸) ∉ 𝜏, (𝐹
2, 𝐸) ∩̃ (𝐹
7, 𝐸) ∉ 𝜏,
(𝐹2, 𝐸) ∪̃ (𝐹
7, 𝐸) ∉ 𝜏, (𝐹
6, 𝐸) ∩̃ (𝐹
14, 𝐸) ∉ 𝜏, (𝐹
6, 𝐸) ∪̃ (𝐹
14,
𝐸) ∉ 𝜏, (𝐹14, 𝐸) ∩̃ (𝐹
15, 𝐸) ∉ 𝜏, (𝐹
14, 𝐸) ∪̃ (𝐹
15, 𝐸) ∉ 𝜏, and
many of the soft sets belong to the family 𝜏 and their softintersection and soft union do not exist in 𝜏. Consequently, [1,Examples 25, 30, 31, 32] also are incorrect. Also, the authorsused the same Example 14 in [2, Example 1], so [2, Examples2, 6, 7, 8] also are incorrect.
Conflict of Interests
There is no conflict of interests regarding the publication ofthis paper.
References
[1] M. Akdag and A. Ozkan, “Soft 𝛼-open sets and soft 𝛼-continuous functions,” Abstract and Applied Analysis, vol. 2014,Article ID 891341, 7 pages, 2014.
[2] M. Akdag and A. Ozkan, “Soft b-open sets and soft b-continuous functions,”Mathematical Sciences, vol. 8, article 124,2014.
Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2015, Article ID 913034, 1 pagehttp://dx.doi.org/10.1155/2015/913034
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