Recent content by h20o85

Thank you for replying (I am new to this forum and I just realized that I am not supposed to ask homework-style questions here...) R is also considered as a normed space, but v is not necessarily a finite dimensional space, therefore I can't use boundedness...

hi guys, I have a question I would like assistance with: let (v,||.||) be a norm space over ℝ, and let f:v→ℝ be a linear functional. if f is continuous on 0 (by the metric induced by the norm), prove that there is k>0 such that for each u in v, |f(u)| ≤ k*||u||. thanks :)