Let n ≥ 2 and 0 < p < 1. For x € K", let ||²||p = [Σ;=1 |Z(j)P)]¹/P. 5-12 Then the set {z € K" : ||||p ≤ 1} is not conve

[answerhappygod]

1 (32.95 KiB) Viewed 47 times

Let n ≥ 2 and 0 < p < 1. For x € K", let ||²||p = [Σ;=1 |Z(j)P)]¹/P. 5-12 Then the set {z € K" : ||||p ≤ 1} is not convex and || ||p is not a norm on K". 5-13 Let Y be a subspace of a normed space X. Then Y is nowhere dense in X (that is, the interior of the closure of Y is empty) if and only if Y is not dense in X. If Y is a hyperspace in X, then Y is nowhere dense in X if and only if Y is closed in X.