Fréchet normal cone (${\hat{N}}_C(z)$)

A vector $w$ is a regular normal at $z\in C$ when ${\mathrm{limsup}}_{z^{\prime }\to z,z^{\prime }\in C\setminus \{z\}}⟨w,z^{\prime }-z⟩/\Vert z^{\prime }-z\Vert \le 0$. At an isolated point all vectors satisfy this condition. It is the local first-order supporting cone.