Comment on “Soft α-Open Sets and Soft α-Continuous Functions”

الملخص EN

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 (F1,E) ∩~ (F2,E)∉τ, (F1,E) ∪~ (F2,E)∉τ, (F1,E) ∩~ (F11,E)∉τ, (F1,E) ∩~ (F14,E)∉τ, (F1,E) ∪~ (F14,E)∉τ, (F2,E) ∪~ (F5,E)∉τ, (F2,E) ∪~ (F6,E)∉τ, (F2,E) ∩~ (F7,E)∉τ, (F2,E) ∪~ (F7,E)∉τ, (F6,E) ∩~ (F14,E)∉τ, (F6,E) ∪~ (F14,E)∉τ, (F14,E) ∩~ (F15,E)∉τ, (F14,E) ∪~ (F15,E)∉τ, and 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.