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edited Aug 19, 2020 at 1:06

Under which conditions the domain of the surjective function $f:[a,b]\times[c,d]\to[0,1]^{2}$ can be split s.t. the restrictions are bijective?

Since it is not always possible to construct such partition, I would like to know if there are additional restrictions which we could impose so that the wanted partition exists in the $n$-dimensional setting ($n\geq 1$).

This is a follow-up question to this.

asked Aug 18, 2020 at 19:37

user127351