Netto's theorem
id:
netto-s-theorem-295-5100490
title:
Netto's theorem
text:
In mathematical analysis, Netto's theorem states that continuous bijections of smooth manifolds preserve dimension. That is, there does not exist a continuous bijection between two smooth manifolds of different dimension. It is named after Eugen Netto. The case for maps from a higher-dimensional manifold to a one-dimensional manifold was proven by Jacob Lüroth in 1878, using the intermediate value theorem to show that no manifold containing a topological circle can be mapped continuously and bij
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wiki
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encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Netto%27s_theorem
date created:
date modified:
2023-06-27T18:49:14Z
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13
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