Equivalence of Smooth Structures
Let and be two maximal atlases on M. The two smooth structures associated to and are said to be equivalent if there is a homeomorphism such that .
Read more about this topic: Smooth Structure
Famous quotes containing the words smooth and/or structures:
“We are born with luck
which is to say with gold in our mouth.
As new and smooth as a grape,
as pure as a pond in Alaska,
as good as the stem of a green bean
we are born and that ought to be enough....”
—Anne Sexton (1928–1974)
“The American who has been confined, in his own country, to the sight of buildings designed after foreign models, is surprised on entering York Minster or St. Peter’s at Rome, by the feeling that these structures are imitations also,—faint copies of an invisible archetype.”
—Ralph Waldo Emerson (1803–1882)