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Homeomorphic extention of a discrete function

Let $f : \\{ 0;1 \\} ^ {n} \rightarrow \\{ 0;1 \\} ^ {n}$ bijective is there a known computable way to extend it into an homeomorphism of: $\[ 0;1 \] ^ {n} \rightarrow \[ 0;1 \] ^ {n}$