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Manifold

| nosplit | ↑ parent "Topology" | words: 164 | descendant words: 424 | descendants: 6
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We map each point and a small enough neighbourhood of it to , so we can talk about the manifold points in terms of coordinates.
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Does not require any further structure besides a consistent topological map. Notably, does not require metric nor an addition operation to make a vector space.
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Manifolds are cool.
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A notable example of a Non-Euclidean geometry manifold is the space of generalized coordinates of a Lagrangian. For example, in a problem such as the double pendulum, some of those generalized coordinates could be angles, which wrap around and thus are not euclidean.
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Ancestors

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