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What are manifolds?

What are manifolds? Here are some definitions.

Noun
  1. plural of manifold
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Examples
One stir plate is pretty much like another, ditto the separatory funnels flasks, vacuum manifolds, etc.
The rules require all cylinder blocks, heads and intake manifolds to have factory part numbers.
It is generally regarded as a study of the iteration of maps, of time evolution of differential equations, and of group actions on manifolds.
The exhaust manifolds are dual-skin, with stainless steel inners.
In addition to instrument panels, magnesium has been used in intake manifolds, valve covers, seat frames, steering wheels, door frames.
My primary interest in geometry is for the light it sheds on the topology of manifolds.

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