The ambient space, in mathematics, is the space surrounding a mathematical object. For example, a line may be studied in isolation, or it may be studied as an object in two-dimensional space -- in which case the ambient space is the plane, or as an object in three-dimensional space -- in which case the ambient space is three dimensional. To see why this makes a difference, consider the statement "Lines that never meet are necessarily parallel." This is true if the ambient space is two dimensional, but false if the ambient space is three dimensional, because in the latter case the lines could be skew lines, rather than parallel.

Reference to the ambient space is important in geometry and, especially, topology. Geometry