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 .
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Famous quotes containing the words smooth and/or structures:
“The island dreams under the dawn
And great boughs drop tranquillity;
The peahens dance on a smooth lawn,
A parrot sways upon a tree,
Raging at his own image in the enamelled sea.”
—William Butler Yeats (1865–1939)
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)