Neighbourhood Basis

Definition: Neighbourhood Basis

Let $(X,\tau )$ be a topological space and let $p\in X$.

A collection $\mathcal{B}$ of neighbourhoods of $p$ is a neighbourhood basis of $(X,\tau )$ at $p$ iff for each ^neighbourhood-of-a-point $N(p)$, there exists some neighbourhood $B(p)\in \mathcal{B}$ such that $B(p)\subseteq N(p)$.