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

Let $f : \{ 0,1 \} ^ {n} \rightarrow \{ 0,1 \} ^ {n}$ be a bijective map. Then is there a known computable way to extend it to a homeomorphism $g:[ 0,1 ] ^ {n} \rightarrow [ 0,1 ] ^ {n}?$

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

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