Corrigendum to: “On soft preopen sets and soft pre separation axioms, Gazi University Journal of Science, 27(4) (2014), 1077- 1083.”

Abstract

The authors of [1] concluded in Example 1 that 𝜏 is a soft topology over 𝑋 = {𝑥1, 𝑥2, 𝑥3, 𝑥4} with respect to the set of attributes 𝐸 = {𝑒1,𝑒2,𝑒3}. In fact, their conclusion is incorrect. For instance, the soft sets (𝐹13, 𝐸) and (𝐹14, 𝐸) are in the collection 𝜏 but (𝐻, 𝐸) = (𝐹13, 𝐸) ∪̃ (𝐹14, 𝐸) where (𝐻, 𝐸) = {(𝑒1,{𝑥1}), (𝑒2,{𝑥2, 𝑥3, 𝑥4}), (𝑒3,{𝑥1, 𝑥2})} not belongs to the same collection 𝜏. In order to achieve the goal of [1, Example 1], let 𝑋 = {𝑥1, 𝑥2, 𝑥3, 𝑥4, 𝑥5} be a universe and 𝐸 = {𝑒} be the singleton attributes set. Define the collection 𝜏 = {∅̃, 𝑋̃, (𝐹1, 𝐸), (𝐹2, 𝐸), (𝐹3, 𝐸)}, where (𝐹1, 𝐸), (𝐹2, 𝐸) and (𝐹3, 𝐸) are soft sets over 𝑋 defined as follows.