Submanifolds of Euclidean Space
Manifolds are often defined as embedded submanifolds of Euclidean space Rn, so this forms a very important special case. By the Whitney embedding theorem any second-countable smooth n-manifold can be smoothly embedded in R2n.
Read more about this topic: Submanifold
Famous quotes containing the word space:
“The flattering, if arbitrary, label, First Lady of the Theatre, takes its toll. The demands are great, not only in energy but eventually in dramatic focus. It is difficult, if not impossible, for a star to occupy an inch of space without bursting seams, cramping everyone elses style and unbalancing a play. No matter how self-effacing a famous player may be, he makes an entrance as a casual neighbor and the audience interest shifts to the house next door.”
—Helen Hayes (19001993)