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. Washington, DC: Math. Assoc. Amer., p. 101, 1967. Krantz,
S. G. "The Concept of Homeomorphism." §6.4.1 in Handbook
of Complex Variables. Boston, MA: Birkhäuser, p. 86, 1999. Ore,
Ø. Graphs
and Their Uses. New York: Random House, 1963. Referenced on Wolfram|Alpha Homeomorphism
Cite this as:
Weisstein, Eric W. "Homeomorphism." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Homeomorphism.html
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