Tangent Spaces and Submersions

This lecture covers the concept of tangent spaces and submersions in differential geometry, focusing on the dimension of vector subspaces and the proposition of tangent spaces at a point of a subvariety. The instructor explains the adaptation to differentiable manifolds and the alerts between them, emphasizing the vector space properties and the proposition of tangent spaces. The lecture also delves into the differentiable structures and the proposition of tangent spaces at a point of a submanifold, highlighting the alerts between them. Moreover, it discusses the alerts between vectors and the proposition of tangent spaces, showcasing the adaptation to differentiable manifolds.