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In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles .
An example of waterfall charts. Here, there are 3 total columns called Main Column1, Middle Column, and End Value. The accumulation of successive two intermediate columns from the first total column (Main Column1) as the initial value results in the 2nd total column (Middle Column), and the rest accumulation results in the last total column (End Value) as the final value.
Gran Atlas Aguilar (Spain, 1969/1970) Historical Atlas of China (Taiwan, 1980) The Historical Atlas of China (China, 1982) National Geographic Atlas of the World (United States, 1963–present) Pergamon World Atlas (1962/1968) Times Atlas of the World (United Kingdom, 1895–present) Dorling Kindersley Atlas of the World 1994–present
This atlas contains every chart that is compatible with the smooth structure. There is a natural one-to-one correspondence between smooth structures and maximal smooth atlases. Thus, we may regard a smooth structure as a maximal smooth atlas and vice versa. In general, computations with the maximal atlas of a manifold are rather unwieldy.
For any integer k > 0 and any n−dimensional C k −manifold, the maximal atlas contains a C ∞ −atlas on the same underlying set by a theorem due to Hassler Whitney.It has also been shown that any maximal C k −atlas contains some number of distinct maximal C ∞ −atlases whenever n > 0, although for any pair of these distinct C ∞ −atlases there exists a C ∞ −diffeomorphism ...
A woman in Kentucky surprised her Navy husband with a special military homecoming by gifting him a five-day duck hunting trip in Kansas with his best friends ahead of Christmas.
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A cartogram (also called a value-area map or an anamorphic map, the latter common among German-speakers) is a thematic map of a set of features (countries, provinces, etc.), in which their geographic size is altered to be directly proportional to a selected variable, such as travel time, population, or gross national income. Geographic space ...