Need help to prove hyperplanes between convex sets

[thelazyman]

Hi,

I need help with this problem.

Prove that a hyperplane H belonging to R^n and its associated half-spaces h^+ and H^- are convex sets.

 

[royhaas]

Use the definition which says that a set is convex if, for each \(\displaystyle x, y\) in the set and every \(\displaystyle 0 \le t \le 1\), \(\displaystyle tx+(1-t)y\) is in the set.