Category:Nets (Topology)

This category contains results about topological nets.
Definitions specific to this category can be found in Definitions/Nets (Topology).

Let $M = \struct {A, d}$ be a metric space.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

An $\epsilon$-net for $M$ is a subset $S \subseteq A$ such that:

$\ds A \subseteq \bigcup_{x \mathop \in S} \map {B_\epsilon} x$

where $\map {B_\epsilon} x$ denotes the open $\epsilon$-ball of $x$ in $M$.