On the separately open topology

We consider the relationship between separately continuous functions and separately open sets, and we study the properties of the separately open topology on R2 and on Q2. We show that R2 with this topology (denoted R ⊗R) is completely and strongly Hausdorff and that Q⊗Q is normal but not a p-space. In addition, we show that each point of Q ⊗Q has an uncountable neighborhood base.