In Chapter 3 we defined manifolds in ℝ n (see Definition 3.3.1), and we remarked that a more abstract definition is possible, so that a manifold does not have to exist in any ℝ n . We introduce this definition in this chapter, and also a technical tool useful in the study of manifolds, called partitions of unity. The chapter closes with an application to the generation of topographic maps.
KeywordsSmooth Manifold Open Disk Mountain Pass View Direction Coordinate Chart
Unable to display preview. Download preview PDF.