Show that a function F mapping D Rn into Rn is continuous at x0 D precisely when, given any number 0, a number 0 can be found with property that for any vector norm , F(x) F(x0) , whenever x D and x x0 ...

Let Fx fix fnx Suppose F is c ...

Show that a function F mapping D Rn into Rn is continuous at x0 D

Question:

Show that a function F mapping D ⊂ Rn into Rn is continuous at x0 ∈ D precisely when, given any number ε > 0, a number δ > 0 can be found with property that for any vector norm ||·||,
||F(x) − F(x0)|| < ε,
whenever x ∈ D and || x − x0 || < δ.