Smooth Structure - Equivalence of Smooth Structures

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:

    Beautiful women seldom want to act. They are afraid of emotion and they do not try to extract anything from a character that they are portraying, because in expressing emotion they may encourage crow’s feet and laughing wrinkles. They avoid anything that will disturb their placidity of countenance, for placidity of countenance insures a smooth skin.
    Laurette Taylor (1887–1946)

    It is clear that all verbal structures with meaning are verbal imitations of that elusive psychological and physiological process known as thought, a process stumbling through emotional entanglements, sudden irrational convictions, involuntary gleams of insight, rationalized prejudices, and blocks of panic and inertia, finally to reach a completely incommunicable intuition.
    Northrop Frye (b. 1912)