Definition:Neighborhood Sub-Basis

Definition

Let $\struct {S, \tau}$ be a topological space.

Let $x \in S$.

Let $\BB$ be a set of neighborhoods of $x$.

Then $\BB$ is a neighborhood sub-basis of $x$ relative to $\tau$ if and only if:

for each neighborhood $N$ of $x$, there exists a finite subset $K$ of $\BB$ such that $\bigcap K \subseteq N$.

Also see

• Definition:Neighborhood Basis
• Definition:Local Sub-Basis