# Category:Definitions/Nets (Topology)

This category contains definitions related to nets in the context of Topology.
Related results can be found in Category:Nets (Topology).

Let $M = \left({A, d}\right)$ 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:

$\displaystyle A \subseteq \bigcup_{x \mathop \in S} B_\epsilon \left({x}\right)$

where $B_\epsilon \left({x}\right)$ denotes the open $\epsilon$-ball of $x$ in $M$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Nets (Topology)"

The following 2 pages are in this category, out of 2 total.