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.