Lineare Algebra 2/Gemischte Definitionsabfrage/15/Aufgabe/Lösung

${\displaystyle {}{\mathbb {C} }^{n}}$

${\displaystyle {}\left\langle u,v\right\rangle :=\sum _{i=1}^{n}u_{i}{\overline {v_{i}}}\,}$

gegeben.

${\displaystyle {}x}$

${\displaystyle {}[x]={\left\{y\in M\mid y\sim x\right\}}\,.}$

${\displaystyle {}U\subseteq M}$

${\displaystyle {}x\in U}$

${\displaystyle {}\epsilon >0}$

${\displaystyle {}U{\left(x,\epsilon \right)}\subseteq U\,}$

existiert.