In the paper titled “Soft α-Open Sets and Soft α-Continuous Functions” [1, Example 14], the authors deduced that is a soft topology over with respect to . In fact, their conclusion is not true. For example, the soft sets and are in the collection but their soft intersection and soft union do not belong to it. It follows that all examples based on Example 14 also are incorrect. The examples of [1] can be replaced by the following accurate examples.
Example 1. Let , , and is a soft topology over with respect to , where is a soft set over defined by . Then the soft set defined by is soft -open set but not soft open set.
Example 2. Let , , and is a soft topology over with respect to , where , and are soft sets over defined as follows:Then the soft set defined by is soft semiopen set but not soft -open set.
Example 3. Let , , and is a soft topology over with respect to , where , , and are soft sets over defined as follows:Then the soft set defined byis soft preopen set but not soft -open set.
Example 4. (1) Let be an injective soft function from an indiscrete soft topological space into discrete soft topological space . Then is soft precontinuous function but not soft -continuous.
(2) Let be the initial universe and , are the parameters sets. If is a soft topology on , where , , and are soft sets defined as follows,and is the discrete soft topology on with respect to , let be a soft function defined byThen is soft semicontinuous but not soft -continuous function.
(3) Let , , and is a soft topology on with respect to the parameters set , where is a soft set on defined by . Then the soft function defined byis soft -continuous but not soft continuous function.