Here is something about invertible functions… Read the section carefully….
In the first point I said that F maps a set of n dimension to a set of same dimension but indeed it could be pf any dimension what is in the range set and indeed for making it a invertible one we indeed need same dimensional sets for upto simplicity…. We may use different dimensions but definition of the function would be in limiting case as for Hilbert Space filling Curves… But That is a different issue….Read these sections carefully …
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Eau dé Mathematica 