Marden, Albert School of Mathematics, University of Minnesota, Minneapolis, Minnesota.
Morgan, John W. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York.
Last reviewed:January 2021
- General topology
- Topological spaces
- Continuous maps and homeomorphisms
- Spaces with special properties
- Algebraic topology
- Euler characteristic
- Fundamental group
- Homotopy theory
- Manifold theory
- Examples of manifolds
- Smooth manifolds
- Homology groups of manifolds
- Classification of manifolds
- Three-dimensional manifolds
- Four-dimensional manifolds
- Related Primary Literature
- Additional Reading
The branch of mathematics that studies the qualitative properties of spaces, as opposed to the more delicate and refined geometric or analytic properties. While there are earlier results that belong to the field, the beginning of the subject as a separate branch of mathematics dates to the work done 1895–1904 by Henri Poincaré. The ideas and results of topology have a central place in mathematics, with connections to almost all the other areas of the subject.
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