Formal Definition of Atlas
An atlas for a topological space M is a collection of charts on M such that . If the range of each chart is the n-dimensional Euclidean space, then M is said to be an n-dimensional manifold.
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“It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between ideas and things, both of which he assumes as given; he need not inquire whether either sphere is real or whether, in the final analysis, reality consists in their interaction.”
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