# Category:Metric Subspaces

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This category contains results about **Metric Subspaces**.

Let $\struct {A, d}$ 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 $\forall x, y \in H: \map {d_H} {x, y} = \map d {x, y}$.

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

The metric space $\struct {H, d_H}$ is called a **metric subspace of $\struct {A, d}$**.

## Pages in category "Metric Subspaces"

The following 9 pages are in this category, out of 9 total.