homeomorphism
noun
ho·meo·mor·phism
ˌhō-mē-ə-ˈmȯr-ˌfi-zəm 
: a function that is a one-to-one mapping between sets such that both the function and its inverse are continuous and that in topology exists for geometric figures which can be transformed one into the other by an elastic deformation
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This is an even stronger statement than the one Freedman proved — since a diffeomorphism is a stronger form of equivalence than a homeomorphism — and one that mathematicians today have no idea how to settle.
—
Quanta Magazine, 28 Sep. 2021
For topological manifolds, the relevant standard is called a homeomorphism.
—Quanta Magazine, 28 Sep. 2021
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Quanta Magazine, 28 Sep. 2021
For topological manifolds, the relevant standard is called a homeomorphism.
—Quanta Magazine, 28 Sep. 2021
Cite this Entry
“Homeomorphism.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/homeomorphism. Accessed 13 Jul. 2025.
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