# Cone condition

In mathematics, the **cone condition** is a property which may be satisfied by a subset of an 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".

## Formal definitions

An open subset of an Euclidean space is said to satisfy the *weak cone condition* if, for all , the cone is contained in . Here 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 of such that for each there exists a cone such that .

## References

- Voitsekhovskii, M.I. (2001), "Cone condition", in Hazewinkel, Michiel,
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4

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