A homeomorphism between topological spaces is a continuous bijection
with a continuous inverse. Homeomorphisms induce an
equivalence relation on topological
spaces . A homeomorphism that also preserves distances
is an isometry . Invertible affine
transformations are examples.
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
in the MathWorld classroom
Explore with Wolfram|Alpha
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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