4.1 Basic Topological Concepts

This section introduces basic topological concepts that are helpful in understanding configuration spaces. Topology is a challenging subject to understand in depth. The treatment given here provides only a brief overview and is designed to stimulate further study (see the literature overview at the end of the chapter). To advance further in this chapter, it is not necessary to understand all of the material of this section; however, the more you understand, the deeper will be your understanding of motion planning in general.

- 4.1.1 Topological Spaces
- Closed sets
- Special points
- Some examples
- Continuous functions
- Homeomorphism: Making a donut into a coffee cup

- 4.1.2 Manifolds
- Manifold definition
- Cartesian products
- 1D manifolds
- Identifications
- 2D manifolds
- Higher dimensional manifolds

- 4.1.3 Paths and Connectivity

Steven M LaValle 2012-04-20