Metric Space Functions

Why

We want to talk about functions from one set with a metric into another set with a metric.

Definition

A function from a first metric space to a second metric space is a function from the first set to the second set.

Notation

Suppose $(A, d)$ and $(B, d')$ be metric spaces. We denote that $f$ is a function from the first metric space to the second metric space by 0 $f: (A, d) \to (B, d')$.