Metric subspace

Definition

Given a metric space $(X,d)$ and any $A\subset X$, we can define a metric as follows:

$$d_A:A\times A\rightarrow\mathbb{R}$$ where $$d_A(x,y)\mapsto d(x,y)$$ (so a restriction of the function essentially)

Then $(A,d_A)$ is a metric subspace of $(X,d)$ and $d_H$ is the induced metric.

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TODO: proof it is a metric space

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