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. For example, a 1-dimensional line ( l ) {\displaystyle (l)} may be studied in isolation —in which case the ambient space of l {\displaystyle l} is the real line, or it may be studied as an object embedded in 2-dimensional Euclidean space ( R 2 ) {\displaystyle (\mathbb {R} ^{2})} —in which case the ambient space of l {\displaystyle l} is R 2 {\displaystyle \mathbb {R} ^{2}} , or as an object embedded in 2-dimensional hyperbolic space ( H 2 ) {\displaystyle (\mathbb {H} ^{2})} —in which case the ambient space of l {\displaystyle l} is H 2 {\displaystyle \mathbb {H} ^{2}} .

Source: Wikipedia — Ambient space (mathematics) (CC BY-SA 4.0)