Everything about Differential Structure totally explained
In
mathematics, an
n-dimensional
differential structure (or differentiable structure) on a set
M makes it into an
n-dimensional
differential manifold, which is a
topological manifold with some additional structure that allows us to do
differential calculus on the manifold. If
M is already a topological manifold, we require that the new topology be identical to the existing one.
Definition
For a natural number
n and some
k which may be a non-negative integer or infinity, an
n-dimensional Ck differential structure is defined using a
Ck-atlas, which is a set of bijections called
charts between a collection of subsets of
M (whose union is the whole of
M), and a set of open subsets of an
n-dimensional
vector space:
» having uncountably many differential structures
Further Information
Get more info on 'Differential Structure'.
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