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.