Exercises
[10S]Prerequisites:[0ZX],[19C],[10F].Let \(r{\gt}0\); if \(p∈[1,∞]\) then the ball \(B_ r^ p=\{ \| x\| _ p{\lt} r\} \) is convex; also \(B_ r^ p⊆ B_ r^{\tilde p}\) if \(\tilde p{\gt} p\). In the case \(n=2\) of planar balls, study graphically the shape of the balls as \(p\) varies. Are there points that are on the border of all balls?
Solution 1