An open subset S of a Euclidean space E is said to satisfy the weak cone condition if, for all \boldsymbol{x} \in S, the cone \boldsymbol{x} + V_{\boldsymbol{e}(\boldsymbol{x}),\, h} is contained in S. Here V_{\boldsymbol{e}(\boldsymbol{x}),h} represents a cone with vertex in the origin, constant opening, axis given by the vector \boldsymbol{e}(\boldsymbol{x}), and height h \ge 0.
