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by anderson1993 1737 days ago
Does anyone know what theorems/definitions this paragraph is referring to?

"Finally, in 1912, almost half a century after Cantor’s discovery, and after many failed attempts to prove the invariance of dimension, L.E.J. Brouwer succeeded by employing some methods of his own creation. In essence, he proved that it is impossible to put a higher-dimensional object inside one of smaller dimension, or to place one of smaller dimension into one of larger dimension and fill the entire space, without breaking the object into many pieces, as Cantor did, or allowing it to intersect itself, as Peano did."

1 comments

The Jordan-Brouwer Separation Theorem - which rigorously defines an inside and outside for higher dimensional objects. http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/...