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Is there a simple geometric proof that there exists a continuous bijective function between a square and its side?
And is there some explicit continuous function or formula $f^1(z)\mapsto (x,y)$ and $f(x,y)\mapsto z$, with $(x,y) \in [0,1]\times[0,1]$ and $z \in [0,1]$?
And is there a constru...