Homeomorphisms

In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.

thumb|right|250px|A Koch snowflake has an infinitely repeating self-similarity when it is magnified. thumb|300px|Standard (trivial) self-similarity

concept in graph theory

object of study in the category of topological spaces

property which occurs on sufficiently small or arbitrarily small neighborhoods of points

theorem in topology about homeomorphic subsets of Euclidean space

mathematical function revertible near each point

problem in geometric topology

Group of isotopy classes of a topological automorphism group

concept in topology

theorem in complex analysis that a conformal mapping sending the unit disk to a region in the complex plane bounded by a Jordan curve extends continuously to a homeomorphism from the unit circle onto the Jordan curve

homeomorphism between plane domains