## ::Supporting hyperplane

### ::concepts

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In geometry, a **supporting hyperplane** of a set <math>S</math> in Euclidean space <math>\mathbb R^n</math> is a hyperplane that has both of the following two properties:

- <math>S</math> is entirely contained in one of the two closed half-spaces bounded by the hyperplane
- <math>S</math> has at least one boundary-point on the hyperplane.

Here, a closed half-space is the half-space that includes the points within the hyperplane.

**Supporting hyperplane sections**

Intro Supporting hyperplane theorem See also References

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Convex::right Boundary::first Theorem::closed Category::point Title::thumb Space::geometry

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In geometry, a **supporting hyperplane** of a set <math>S</math> in Euclidean space <math>\mathbb R^n</math> is a hyperplane that has both of the following two properties:

- <math>S</math> is entirely contained in one of the two closed half-spaces bounded by the hyperplane
- <math>S</math> has at least one boundary-point on the hyperplane.

Here, a closed half-space is the half-space that includes the points within the hyperplane.

**Supporting hyperplane sections**

Intro Supporting hyperplane theorem See also References

PREVIOUS: Intro | NEXT: Supporting hyperplane theorem |

<< | >> |