Manifolds

What is manifold?
Manifold is a set, and also a topological space
Smoothness
Smooth structure
Definition of manifold
Equivalence relation on atlases
Smooth maps between manifolds
The notion of o-little
Cotangent space
Tangent space
Tangent bundle
Tangent bundle: transition functions
Consistency condition on the transition functions
Derivatives of maps
Category of smooth manifolds



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