Manifolds with Boundary
According to our definition of C r manifold, given in Chapter 2, we cannot use our “differential topology tool kit” for many interesting sets such as a closed unit ball, a solid torus, a compact cylindrical surface. Those sets fail to be C r manifolds because of points they have on their “boundaries”. In fact, around those points they look like closed euclidean halfspaces or even convex cones. The definition of manifold with boundary deals with this issue, encompassing a wider class of objects which includes some of the examples we have just referred to.
KeywordsOpen Subset Tangent Space General Equilibrium Local Parametrization Inverse Image
Unable to display preview. Download preview PDF.