Ambient space (mathematics)

In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object along with the object itself.

may be studied in isolation —in which case the ambient space of

, or it may be studied as an object embedded in 2-dimensional Euclidean space

—in which case the ambient space of

, or as an object embedded in 2-dimensional hyperbolic space

To see why this makes a difference, consider the statement "Parallel lines never intersect."

This is true if the ambient space is

, but false if the ambient space is

are different from the geometric properties of

This geometry-related article is a stub.