Abstract and Applied Analysis
Volume 2015 (2015), Article ID 329509, 2 pages
http://dx.doi.org/10.1155/2015/329509

Corrigendum

Corrigendum to “Soft -Open Sets and Soft -Continuous Functions”

Metin Akdag,¹ Alkan Ozkan,¹ A. Ghareeb,² and A. K. Mousa³

¹Department of Mathematics, Science Faculty, Cumhuriyet University, Sivas, Turkey
²Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
³Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

Received 17 September 2015; Accepted 29 October 2015

Copyright © 2015 Metin Akdag et al. 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.

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 by

is 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 by

Then 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 by

is soft -continuous but not soft continuous function.

References

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.