use the following concepts: In the metric space Rn with the usual Euclidean metric, we can define a linear structure by setting (x 1 ,…., x n ) + ( y 1 ,…., y n ) = (x 1 + y 1 ,…., x n + y n ) And λ...

use the following concepts: In the metric space Rn with the usual Euclidean metric, we can define a linear structure by setting

(x₁,…., x_n
) + ( y₁,…., y_n
) = (x₁
+ y₁,…., x_n
+ y_n
)

And

λ (x₁,…., x_n
) = (λx₁,….,λx_n
)

for arbitrary points x = (x₁, …, x_n) and y = (y₁, …, y_n) in Rn and for λ ∈
.

Let λ ∈
. Prove that f :

ⁿ
→

ⁿ
defined by f (x) = λx is continuous on Rn