topology
Sign in to savethumb|upright=1.5|A three-dimensional model of a Figure-eight knot (mathematics)|figure-eight knot. The figure-eight knot is a [[prime knot and has an Alexander–Briggs notation of 41.]]
AI overview
Topology is a branch of mathematics that studies properties of objects and shapes that remain unchanged even when they are bent, stretched, or twisted without tearing or gluing. It matters because it helps mathematicians understand the fundamental characteristics of shapes and spaces in ways that go beyond traditional geometry.
AI-generated from the Wikipedia summary — may contain errors.
Article
28 sectionsContents
- Motivation
- History
- Concepts
- Topologies on sets
- Continuous functions and homeomorphisms
- Manifolds
- Subfields
- General topology
- Algebraic topology
- Differential topology
- Geometric topology
- Generalizations
- Applications
- Biology
- Computer science
- Physics
- Robotics
- Games and puzzles
- Fiber art
- Resources and research
- Major journals
- Major books
- See also
- References
- Citations
- Bibliography
- Further reading
- External links
thumb|upright=1.5|A three-dimensional model of a Figure-eight knot (mathematics)|figure-eight knot. The figure-eight knot is a [[prime knot and has an Alexander–Briggs notation of 41.]]
Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.