Explore Homotopy on MathWorld

A continuous deformation of a topological space or a function between two topological spaces.

Homotopy is a graduate-level concept that would be first encountered in a topology course.


Continuous Function: A continuous function is function with no jumps, gaps, or undefined points.
Topology: (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties.

Classroom Articles on Topology (Up to Graduate Level)

  • Closed Set
  • Neighborhood
  • Differential Topology
  • Open Set
  • Dimension
  • Point-Set Topology
  • Homeomorphism
  • Projective Plane
  • Homology
  • Projective Space
  • Knot
  • Subspace
  • Link
  • Tangent Space
  • Manifold
  • Topological Space
  • Metric
  • Torus
  • Metric Space
  • Vector Bundle
  • Möbius Strip