Soft -Open Sets and Soft -Continuous Functions - Downloads

Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2015, Article ID 913034, 1 page http://dx.doi.org/10.1155/2015/913034

Letter to the Editor Comment on (Soft 𝛼-Open Sets and Soft 𝛼-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 Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Akdag and Ozkan pointed out in [1, Example 14] that the collection 𝜏 of soft sets is a soft topology over the universe 𝑋 = {𝑥1 , 𝑥2 , 𝑥3 , 𝑥4 }, where 𝐸 = {𝑒1 , 𝑒2 , 𝑒3 } is the set of parameters. This conclusion is not correct since ̃ (𝐹2 , 𝐸) ∉ 𝜏, (𝐹1 , 𝐸) ∪ ̃ (𝐹2 , 𝐸) ∉ 𝜏, (𝐹1 , 𝐸) ∩ ̃ (𝐹11 , (𝐹1 , 𝐸) ∩ ̃ ̃ 𝐸) ∉ 𝜏, (𝐹1 , 𝐸) ∩ (𝐹14 , 𝐸) ∉ 𝜏, (𝐹1 , 𝐸) ∪ (𝐹14 , 𝐸) ∉ 𝜏, (𝐹2 , ̃ (𝐹6 , 𝐸) ∉ 𝜏, (𝐹2 , 𝐸) ∩ ̃ (𝐹7 , 𝐸) ∉ 𝜏, ̃ (𝐹5 , 𝐸) ∉ 𝜏, (𝐹2 , 𝐸) ∪ 𝐸) ∪ ̃ (𝐹7 , 𝐸) ∉ 𝜏, (𝐹6 , 𝐸) ∩ ̃ (𝐹14 , 𝐸) ∉ 𝜏, (𝐹6 , 𝐸) ∪ ̃ (𝐹14 , (𝐹2 , 𝐸) ∪ ̃ (𝐹15 , 𝐸) ∉ 𝜏, (𝐹14 , 𝐸) ∪ ̃ (𝐹15 , 𝐸) ∉ 𝜏, and 𝐸) ∉ 𝜏, (𝐹14 , 𝐸) ∩ many of the soft sets belong to the family 𝜏 and their soft intersection and soft union do not exist in 𝜏. Consequently, [1, Examples 25, 30, 31, 32] also are incorrect. Also, the authors used the same Example 14 in [2, Example 1], so [2, Examples 2, 6, 7, 8] also are incorrect.

Conflict of Interests There is no conflict of interests regarding the publication of this paper.

References [1] M. Akdag and A. Ozkan, “Soft 𝛼-open sets and soft 𝛼continuous 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 bcontinuous functions,” Mathematical Sciences, vol. 8, article 124, 2014.

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