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banach_space [2014/03/24 19:38]
nikolaj
banach_space [2015/02/03 10:18]
nikolaj
Line 6: Line 6:
 | @#55EE55: postulate ​  | @#55EE55: $\exists v_\infty.\,​\mathrm{lim}_{n\to\infty}\Vert v_n-v_\infty \Vert = 0$ | | @#55EE55: postulate ​  | @#55EE55: $\exists v_\infty.\,​\mathrm{lim}_{n\to\infty}\Vert v_n-v_\infty \Vert = 0$ |
  
-==== Discussion ====+=== Elaboration ​===
 For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm. $\Longleftrightarrow$ The space $\mathcal V$ is complete. For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm. $\Longleftrightarrow$ The space $\mathcal V$ is complete.
 +
 +-----
 === Reference === === Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Banach_space|Banach space]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Banach_space|Banach space]]
-==== Parents ==== + 
-=== Subset of === +-----
-[[Normed vector space]]+
 === Requirements === === Requirements ===
 [[Cauchy sequence]] [[Cauchy sequence]]
 +=== Subset of ===
 +[[Normed vector space]]
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