Let \(X\) be a topological space and \(p\in X\). A neighborhood basis at \(p\) is a collection \(\mathcal B_p\) of neighborhoods of \(p\) such that every neighborhood \(N\) of \(p\) contains some \(B\in\mathcal B_p\).
What is a neighborhood basis at a point $x$?
What collection of open sets forms a neighborhood basis at $x$?