# Definition:Region/Metric Space

## Definition

Let $M = \left({A, d}\right)$ be a metric space.

A **region** of $M$ is a subset $U$ of $M$ such that $U$ is:

- $(1): \quad$ non-empty
- $(2): \quad$ path-connected.

## Also defined as

Some sources insist that in order for a subset of a metric space to be a **region** it must also be open.