Section: STEM · MathematicsDifficulty: Advanced
Topology
USUK
The mathematical study of properties preserved under continuous deformations of objects.
Definition
Topology is a branch of mathematics that studies the properties of geometric objects that remain unchanged under continuous deformations such as stretching, bending, twisting, or crumpling, but not tearing or gluing. Key concepts include open and closed sets, continuity, compactness, and connectedness. Topology has applications in physics, data analysis, robotics, and the study of spacetime.
Example
“In topology, a coffee mug and a donut (torus) are considered equivalent because both have exactly one hole, and one can be continuously deformed into the other without tearing or gluing.”
Synonyms
- rubber sheet geometry
- continuous deformation geometry
- qualitative geometry
Antonyms / Opposites
- rigid geometry
- Euclidean geometry
Images
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Related Terms
- Graph Theory
- Manifold
- Euler Characteristic
- Knot Theory