Comment on “On Soft β-Open Sets and Soft β-Continuous Functions”

Abstract EN

Akdag and Ozkan pointed out in [1, Example 1] that the collection τ of soft sets is a soft topology over the universe X={x1,x2,x3} where E={e1,e2,e3} is the set of parameters.

This conclusion is not correct since (F2,E)∩~(F7,E)∉τ, (F3,E)∪~(F8,E)∉τ, (F1,E)∪~(F13,E)∉τ, (F1,E)∩~(F13,E)∉τ, (F2,E)∩~(F13,E)∩~(F13,E)∉τ, (F2,E)∪~(F13,E)∉τ, (F2,E)∩~(F14,E)∉τ, and many of soft sets belong to the family τ and their soft intersection and soft union do not exist in τ.

Consequently, [1, Examples 27, 28, 29, 30] also are incorrect.

Example 3.3 in [2] already proved the results in [1, Remark 12] and [2, Examples 4.3 and 4.4] also proved the results in [1, Remark 26].