Neighborhood Basis

Last updated Nov 1, 2022

Suppose $(X, \tau)$ is a Topological Space. Then $\mathcal{B}_{x}$ is a Neighborhood Basis for $x \in X$ if

1. $B$ is Open for all $B \in \mathcal{B}_{x}$
2. $x \in B$ for all $B \in \mathcal{B}_{x}$
3. If $U$ is Open and $x \in U$, there exists $B \in \mathcal{B}_{x}$ so that $B \subset U$.

1. A Union of all Neighborhood Bases is a Topological Basis.