Lecture 36 Transversality revisited

We studied properties of the transversality of maps in C^r(M,N) to a fixed submanifold A of N in the beginning of the course. Our point of view was elementary since the topologies in the space of differentiable maps were not available for us yet. Now, we can revisit the subject within the framework of the weak and strong topologies.

We see several interesting results and in particular that if A is closed, the subset of maps in C^r(M,N) that are transverse to A is open and dense for the strong topology.

Lecture notes: