Difference between revisions of "Open ball"
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==Proof that an open ball is open== | ==Proof that an open ball is open== | ||
{{Todo|The proof is really easy, just show a smaller ball fits inside, thus the open ball is a neighborhood to all of its points}} | {{Todo|The proof is really easy, just show a smaller ball fits inside, thus the open ball is a neighborhood to all of its points}} | ||
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| + | ==See Also== | ||
| + | * [[Open set]] | ||
Revision as of 20:51, 12 February 2015
For a metric space [math](X,d)[/math] an "open ball" of radius [math]r[/math] centred at [math]a[/math] is the set
[math]\{x\in X|d(a,x)\lt r\}[/math], it can be denoted several ways. I frequently encounter
[math]B_r(a)=B(a;r)=\{x\in X|d(a,x)\lt r\}[/math] and use [math]B_r(a)[/math]
Proof that an open ball is open
TODO: The proof is really easy, just show a smaller ball fits inside, thus the open ball is a neighborhood to all of its points
