A
homeomorphism is a
topological isomorphism. More precisely, suppose
X and
Y are
topological spaces, and
f is a
function from
X to
Y. Then
f is a homeomorphism
iff all the following hold:
- f is a bijection.
- f is continuous.
- f -1 is continuous.
Two topological spaces are said to be homeomorphic if there is a homeomorphism from one to the other. If two spaces are homeomorphic then they have exactly the same topological properties.
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