closure of a vector subspace in a normed space is a vector subspace
Then, the sequence is a sequence in (because is a vector subspace), and it’s trivial (use properties of the norm) that this sequence converges to , and so this sum is a vector which lies in .
We have proved that is a vector subspace. QED.
|Title||closure of a vector subspace in a normed space is a vector subspace|
|Date of creation||2013-03-22 15:00:16|
|Last modified on||2013-03-22 15:00:16|
|Last modified by||gumau (3545)|