ABSTRACT
The concept of a 2-dimensional surface in 3-dimensional space is intuitively appealing. See Figure 4.1.
The surface is a 2-dimensional geometric object. It could be a hyperplane, as in Figure 4.2. Or it could be something more general (Figure 4.1). The key fact about a 2-dimensional surface is that it is locally like Euclidean 2space. What does this mean? If p is a point of the surface, then there is a neighborhood of p that is homeomorphic to an open set in R2: reference Figure 4.3.
