Category:Definitions/Nets (Topology)

From ProofWiki
Jump to navigation Jump to search

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

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

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


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.