Projective Geometry
In an affine or Euclidean space of higher dimension, the points at infinity are the points which are added to the space to get the projective completion. The set of the points at infinity is called, depending on the dimension of the space, the line at infinity, the plane at infinity or the hyperplane at infinity, in all cases a projective space of one less dimension.
This condition does not depend on the ground field. If real or complex numbers are used, then, from the point of view of differential geometry, points at infinity form a hypersurface, which means a submanifold having one less dimension than the whole projective space. In the general case these facts may be formulated using algebraic manifolds.
Read more about this topic: Point At Infinity
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