Explore Homeomorphism on MathWorld

A homeomorphism is ann equivalence relation and one-to-one correspondence that is continuous in both directions between points in two geometric figures or topological spaces.

Homeomorphism is a college-level concept that would be first encountered in a topology course covering point-set topology.


Geometry: Geometry is the branch of mathematics that studies figures, objects, and their relationships to each other. This contrasts with algebra, which studies numerical quantities and attempts to solve equations.
Topological Space: A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set.

Classroom Articles on Point-Set Topology

  • Closed Set
  • Point-Set Topology
  • Neighborhood
  • Subspace
  • Open Set

  • Classroom Articles on Topology (Up to College Level)

  • Dimension
  • Projective Plane
  • Metric
  • Projective Space
  • Metric Space
  • Topology
  • Möbius Strip
  • Torus