In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold.
Read more about Smooth Structure: Definition, Maximal Smooth Atlases, Equivalence of Smooth Structures, Exotic Spheres, Related Structures
Famous quotes containing the words smooth and/or structure:
“Less smooth than her Skin and less white than her breast
Was this pollisht stone beneath which she lyes prest
Stop, Reader, and Sigh while thou thinkst on the rest
With a just trim of Virtue her Soul was endu’d
Not affectedly Pious nor secretly lewd,
She cut even between the Cocquet and the Prude.”
—Matthew Prior (1664–1721)
“There is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered, or born with. We must give up the idea of a clearly defined shared structure which language-users acquire and then apply to cases.”
—Donald Davidson (b. 1917)