## TerminologyEdit

The open ball in a metric space with radius centered at a, is denoted . Formally

## DefinitionEdit

Let be a metric space. We say a set is open if for every such that .

We say a set is closed if is open.

The open ball in a metric space with radius centered at a, is denoted . Formally

Let be a metric space. We say a set is open if for every such that .

We say a set is closed if is open.