Hypersurface

Encyclopedia : H : HY : HYP : Hypersurface

In mathematics, a hypersurface is some kind of submanifold.

For differential geometry usage, see glossary of differential geometry and topology.
In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set that is purely of dimension n − 1. It is then defined by a single equation F = 0, a homogeneous polynomial in the homogeneous coordinates. (It may have singularities, so not in fact be a submanifold in the strict sense.)

See also: hyperplane, hypersphere, hyperspace.

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