$ \mathbb{X}=\left(\left[0,\omega_{1}\right]\times\left[0,\omega\right]\right)\setminus\left\{ \left(\omega_{1},\omega\right)\right\} $ is not T4

Question

I need to show that the subspace $\mathbb{X}=\left(\left[0,\omega_{1}\right]\times\left[0,\omega\right]\right)\setminus\left\{ \left(\omega_{1},\omega\right)\right\} $ of $\left[0,\omega_{1}\right]\times\left[0,\omega\right]$ with the order topology is not T4 using the sets $A=\left[0,\omega_{1}\right)\times\left\{ \omega\right\} \cap\mathbb{X}, B=\left\{ \omega_{1}\right\} \times\left[0,\omega\right]$.

Now clearly I assumed exists $U,V\subseteq \mathbb{X}$ open sets such that $A\subseteq U, B\subseteq V$ and $U\cap V=\varnothing$. But as of yet, I haven't reached a contradiction.