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.
See also Affine Transformation ,
Homeomorphic ,
Homeomorphic
Graphs ,
Homeomorphic Type ,
Homeomorphism
Group ,
Homomorphism ,
Isometry ,
Module Homomorphism ,
Structure
Homomorphism ,
Topologically Conjugate Explore this topic
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References Coxeter, H. S. M. and Greitzer, S. L. Geometry
Revisited. Krantz,
S. G. "The Concept of Homeomorphism." §6.4.1 in Handbook
of Complex Variables. Ore,
Ø. Graphs
and Their Uses. Referenced on Wolfram|Alpha Homeomorphism
Cite this as:
Weisstein, Eric W. "Homeomorphism." From
MathWorld https://mathworld.wolfram.com/Homeomorphism.html
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