Consider the point $x=\langle \omega_1,\omega\rangle$ in the Tychonov plank $(\omega_1 + 1)\times(\omega + 1)$. Then there is essentially only one sequence (of length $\omega$) converging to it, namely $x_n=\langle \omega_1,n\rangle$ for $n\in\omega$. Indeed, any other sequence converging to $x$ is eventually contained in $\{x_n:n\in\omega\}$. 

My question is: does this property (or any similar one) has a standard name ?