I am studying a little bit of basis (for a Grothendieck topology), following MacLane's Sheaves in Geometry and Logic. Here they give an example as follows,
Let $\mathbf{T}$ be a small category of topological spaces, which is closed under finite limits and under taking open subsets. Define a basis $K$ by taking $\{f_i:Y_i \rightarrow X \mid i \in I\}\in K(X)$ if and only if $f: \amalg Y_i\rightarrow X$ is a open surjection.
They say that to prove that $K$ is a basis, it is enough to prove that the pullback diagram is an open surjection. Why is that?
Thank you so much for your time!