Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
banach_space [2015/02/03 10:18]
nikolaj
banach_space [2015/02/03 10:21] (current)
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: $\exists v_\infty.\,​\mathrm{lim}_{n\to\infty}\Vert v_n-v_\infty \Vert = 0$ |
  
 +-----
 === Elaboration === === 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]]
Link to graph
Log In
Improvements of the human condition