Definition:Neighborhood System

Definition

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

A neighborhood system is a family $\family {\NN_x}_{x \mathop \in S}$ indexed by points of $S$, such that $\NN_x$ is a local basis at $x$ for $x \in S$.

Sources

• 1989: Ryszard Engelking: General Topology (revised and completed ed.)

• Mizar article TOPGEN_2:def 3