On θ-semiopen sets and separation axioms in topological spaces

In 1963, Levine introduced the notion of semi-open sets in topological spaces. In 1968, Velicko introduced ˇ θ-open sets and θ-closure operator. In this paper, we introduce a new notion called θ-semiopen sets which are stronger than semi-open sets but weaker than θ-open sets. Moreover, we investigate some weak separation axioms by making use of θ-semiopen sets and the θ-semi-closure operator.