Open ball on a metric space ↩

Metadata

shorthands: {}
aliases: [ε-neighborhood, Disk on a metric space]
created: 2021-12-15 11:08:42
modified: 2022-01-30 22:18:33

Let

be a metric space.
Given a point

and a real number

, we define the set

As an open ball on , where is called the center and the radius. It is also called a -neighborhood of . ()

We see that every neighborhood of contains .

See also