View source for Metric/Infobox

{{Infobox
|title=Metric
|above=<span style="font-size:2em;">{{M|d:X\times X\rightarrow\mathbb{R}_{\ge 0} }}</span><br/>Where {{M|X}} is any [[set]]
|header1=[[subtypes of topological spaces|relation to other topological spaces]]
|label1=''is a''
|data1=<nowiki/> 
* [[topological space]]
|label2=''contains all''
|data2=<nowiki/>
* [[normed space|normed vector spaces]]
* [[inner product space|inner product spaces]]
|header3=Related objects
|label3=Induced by [[norm]]
|data3=<nowiki/>
* {{M|1=d_{\Vert\cdot\Vert}:V\times V\rightarrow\mathbb{R}_{\ge 0} }}
* {{M|1=d_{\Vert\cdot\Vert}:(x,y)\mapsto\Vert x-y\Vert}}
For {{M|V}} a [[vector space]] over {{M|\mathbb{R} }} or {{M|\mathbb{C} }}
|label4=Induced by [[inner product]]
|data4=<nowiki/>
An [[inner product]] induces a [[norm]]:
* {{M|1=\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:V\rightarrow\mathbb{R}_{\ge 0} }}
* {{M|1=\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:x\mapsto\sqrt{\langle x,x\rangle} }}
Which induces a ''metric'':
* {{M|1=d_{\langle\cdot,\cdot\rangle}:V\times V\rightarrow\mathbb{R}_{\ge 0} }}
* {{M|1=d_{\langle\cdot,\cdot\rangle}:(x,y)\mapsto\sqrt{\langle x-y,x-y\rangle} }}
}}<noinclude>
[[Category:Infoboxes]]
</noinclude>