Open Set

A construct that allows us to take a Directional Derivative from any direction.

Definition

A set $U\subset {\mathbb{R}}^n$ is an open set if: $\forall \text{ point }p\in U,\exists r>0\text{ s.t }{D}_r(p)\subset U$ The neighbourhood of a point $p\in {\mathbb{R}}^n$ is an open set $U$ containing point $p$ Where:

• $D_r$ is the Open Ball