Differential geometry MOC

Tangent bundle

Let be a -manifold. The tangent bundle is a vector bundle of all the tangent spaces of , #m/def/geo/diff so as a set

The construction of topological and -structure is a little more involved. Let be the maximal atlas for , so each gives a -isomorphism

which induces a bijection

which induce an atlas on . Thus is open iff is open for every .

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