Description
Book SynopsisThis is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.
Table of Contents
- The fundamental theorem of algebra
- The Brouwer fixed point theorem
- Tools
- Lebesgue covering dimension
- Fat curves and Peano curves
- The arc, the simple closed curve, and the Cantor set
- Algebraic topology
- Characterization of the 2-sphere
- 2-manifolds
- Arcs in $\mathbb{S}^2$ are tame
- R. L. Moore's decomposition theorem
- The open mapping theorem
- Triangulation of 2-manifolds
- Structure and classification of 2-manifolds
- The torus
- Orientation and Euler characteristic
- The Riemann-Hurwitz theorem
- Bibliography
