topology

Also known as topologically

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.]]

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.

Wikidata facts

Image: Möbius strip.jpg

Show 4 more facts

Commons category: Topology
Commons gallery: Topology
Classification of Instructional Programs code: 27.0105
Stack Exchange tag: physics.stackexchange.com/tags/topology

Sources (6)

via Wikidata · CC0

~23 min read

Article

28 sections

Contents

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.