Metric subspace
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Revision as of 22:45, 8 March 2015 by Alec (Talk | contribs) (Created page with "==Definition== Given a metric space {{M|(X,d)}} and any {{M|A\subset X}}, we can define a metric as follows: <math>d_A:A\times A\rightarrow\mathbb{R}</math>...")
Definition
Given a metric space [ilmath](X,d)[/ilmath] and any [ilmath]A\subset X[/ilmath], we can define a metric as follows:
[math]d_A:A\times A\rightarrow\mathbb{R}[/math] where [math]d_A(x,y)\mapsto d(x,y)[/math] (so a restriction of the function essentially)
Then [ilmath](A,d_A)[/ilmath] is a metric subspace of [ilmath](X,d)[/ilmath] and [ilmath]d_H[/ilmath] is the induced metric.
TODO: proof it is a metric space
