network

Definition

Let N be a subset family of a topologcal space X.
N is called a network of X if for every point x in X and every open set U, there exists some member V in N such that $x\in V\subset U$.

Remark

If N consists of open sets, N is called a base.

Reference

S. Geschke, Applications of elementary submodels in general topology, Foundations of the Formal Sciences, May 7-9, 1999, p.13-20