Reference hyperplane

A pair of support lines at one point.

Reference hyperplane of the set $M$ ${\ displaystyle M}$ $M$ at $n$ ${\ displaystyle n}$ $n$ -dimensional vector space - $(n-1)$ ${\ displaystyle (n-1)}$ $(n-1)$ -dimensional affine subspace that contains closure points $M$ ${\ displaystyle M}$ $M$ and leaves $M$ ${\ displaystyle M}$ $M$ in one closed half-space.

At $n=3$ ${\ displaystyle n = 3}$ $n = 3$ the reference hyperplane is called the reference plane , and when $n=2$ ${\ displaystyle n = 2}$ $n = 2$ - reference line .

Related Definitions

Boundary point of the set $M$ ${\ displaystyle M}$ through which at least one supporting hyperplane passes is called the reference point $M$ ${\ displaystyle M}$ . A convex set $M$ ${\ displaystyle M}$ all its boundary points are reference points. Archimedes used the latter property as a definition of convexity $M$ ${\ displaystyle M}$ .
The boundary points of a convex set $M$ ${\ displaystyle M}$ through which a single supporting hyperplane passes are called smooth .

Links

Alexandrov P.S. Encyclopedia of Elementary Mathematics. T.5. M .: Fizmatlit, 1966. P.193.

Reference hyperplane

Related Definitions

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