# Category:Metric Subspaces

This category contains results about Metric Subspaces.

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

Let $H \subseteq A$.

Let $d_H: H \times H \to \R$ be the restriction $d \restriction_{H \times H}$ of $d$ to $H$.

That is, let $\forall x, y \in H: d_H \left({x, y}\right) = d \left({x, y}\right)$.

Then $d_H$ is the **metric induced on $H$ by $d$** or the **subspace metric of $d$ (with respect to $H$)**.

The metric space $\left({H, d_H}\right)$ is called a **metric subspace of $\left({A, d}\right)$**.

## Pages in category "Metric Subspaces"

The following 8 pages are in this category, out of 8 total.