In mathematics, a hypersurface is some kind of submanifold. Main article: History of mathematics The evolution of mathematics can be seen to be an ever increasing series of abstractions. ... This is a glossary of terms specific to differential geometry and differential topology. ...

• 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. In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... This is a glossary of terms specific to differential geometry and differential topology. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, a projective space is a fundamental construction from any vector space. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... In mathematics, homogeneous has a variety of meanings. ... In mathematics, homogeneous co-ordinates, introduced by August Ferdinand Möbius, make calculations possible in projective space just as Cartesian co-ordinates do in Euclidean space. ... In geometry, a hyperplane is a linear, affine, or projective subspace of codimension 1. ... A hypersphere is a higher-dimensional analogue of a sphere. ... In physics, hyperspace is a theoretical entity. ...