I'm trying to understand the topology of pointwise convergence, we're defined it on the set $\cal{F}(X)$ of real functions on set $X$ to be the sub basis with topology $\{f \in \cal{F}(X) : a < f(x) where $x \in X$ and $a,b \in \mathbb{R}$.
Then it says: 'A set from the sub-basis consists of all functions that pass through one vertical interval'. But at what $x$ value is this interval? And which out of $x,a,b$ are 'changing' to create the sub basis?