: Matemáticas: hypersurface

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geometry > topological space > manifold > topological manifold > hypersurface

geometry > algebraic geometry > algebraic variety > hypersurface

topology > general topology > dimension theory > hypersurface

hypersurface

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. Hypersurfaces share, with surfaces in a three-dimensional space, the property of being defined by a single implicit equation, at least locally (near every point), and sometimes globally.
A hypersurface in a (Euclidean, affine, or projective) space of dimension two is a plane curve. In a space of dimension three, it is a surface.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hypersurface)

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