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Fix typo in atlases documentation
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GregVernon authored Sep 25, 2024
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# [Atlases and charts](@id atlases_and_charts)

Atlases on an ``n``-dimensional manifold ``mathcal M``are collections of charts ``\mathcal A = \{(U_i, φ_i) \colon i \in I\}``, where ``I`` is a (finite or infinite) index family, such that ``U_i \subseteq \mathcal M`` is an open set and each chart ``φ_i: U_i → ℝ^n`` is a homeomorphism. This means, that ``φ_i`` is bijective – sometimes also called one-to-one and onto - and continuous, and its inverse ``φ_i^{-1}`` is continuous as well.
Atlases on an ``n``-dimensional manifold ``\mathcal M``are collections of charts ``\mathcal A = \{(U_i, φ_i) \colon i \in I\}``, where ``I`` is a (finite or infinite) index family, such that ``U_i \subseteq \mathcal M`` is an open set and each chart ``φ_i: U_i → ℝ^n`` is a homeomorphism. This means, that ``φ_i`` is bijective – sometimes also called one-to-one and onto - and continuous, and its inverse ``φ_i^{-1}`` is continuous as well.
The inverse ``φ_i^{-1}`` is called (local) parametrization.
The resulting _parameters_ ``a=φ(p)`` of ``p`` (with respect to the chart ``φ``) are in the literature also called “(local) coordinates”. To distinguish the parameter ``a`` from [`get_coordinates`](@ref) in a basis, we use the terminology parameter in this package.

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