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network

Last-modified: 2010-11-22 (月) 15:53:01

Definition Edit

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 Edit

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

Reference Edit

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