Cone condition

In mathematics, the cone condition is a property which may be satisfied by a subset of a Euclidean space.

Informally, it requires that for each point in the subset a cone with vertex in that point must be contained in the subset itself, and so the subset is "non-flat".

An open subset

{\displaystyle S}

of a Euclidean space

is said to satisfy the weak cone condition if, for all

{\displaystyle {\boldsymbol {x}}\in S}

, the cone

is contained in

represents a cone with vertex in the origin, constant opening, axis given by the vector

, and height

satisfies the strong cone condition if there exists an open cover

there exists a cone such that