Some Strong Forms of Semiseparated Sets and Semidisconnected Space

The concept of semi-open sets in topological spaces was first introduced by Levine. Also the concept of θ-semi-open sets in topological spaces was introduced by Noiri, which is stronger than semi-open sets. Now, we introduce a new type of separated sets called θ-semiseparated sets, which is stronger than semiseparated sets due to Dube and Panwar, and we give some properties of it, furthermore we introduce a new type of disconnectedness interms of θ-semiseparated sets called θ-semidisconnected space, which is stronger than semi-disconnectedness due to Dorsett. Moreover, we give some characterizations and properties of it. It is shown that, a space X is θ-semiconnected if and only if every θs-continuous function from X to the discrete space {0, 1} is constant.