Open ball
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Revision as of 20:27, 12 February 2015 by Alec (Talk | contribs) (Created page with "{{Definition|Topology|Metric Space}} 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...")
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
