Epsilon Neighbourhood

analysis

Definition

Epsilon Umgebung

Epsilon Neighbourhood

The epsilon neighbourhood of $a$ is defined as the open interval:

$$U_{\epsilon }(a)=(a-\epsilon ,a+\epsilon )=\{x\in \mathbb{F}\mid |x-a|<\epsilon \}$$

In other words, the epsilon neighbourhood of $a$ is the set of all points whose distance from $a$ is less than $\epsilon$.