# Homeomorphism

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.

### Prerequisites

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. |