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Homeomorphism

Alternate name

continuous transformation

Basic definition

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.

Detailed definition

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological spaces that is continuous in both directions. A homeomorphism which also preserves distances is called an isometry. Affine transformations are another type of common geometric homeomorphism. The similarity in meaning and form of the words "homomorphism" and "homeomorphism" is unfortunate and a common source of confusion.

Related terms

affine transformation | homeomorphic | homeomorphic type | homeomorphism group | homomorphism | isometry | module homomorphism | structure homomorphism | topologically conjugate

Educational grade level

college level

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