We know that the class of open intervals $(a,b)$, where $a,b$ are rational numbers is a countable base for $\mathbb R$.
But, $[a,b]$ where $a,b$ are rational numbers does not produce a base for $\mathbb R$.
Can we say that any $(a,b)$ or $[a,b]$ where $a$ is rational number and $b$ is an irrational number produce a base for $\mathbb R$?