Let u be a fixed point in and let c be a fixed real number. Prove that each of the following three sets is convex:
By definition of convex, we claim that the line segment is contained in S.
Since by definition of a scalar product, then
The problem I have is that in R, the set (a) would be a line greater than c, set (b) would be a point, and set (c) would be a line lessthan c.
If in , then the set (a) be various regions depending on the signs for ?