Let $I$ a compact set and $f\in\mathcal{C}([0,1]^I)$. Then exists $J\subset I$, countable or finite, such that:
if $x,y\in [0,1]^I$ such that $x\big|_J=y\big|_J\Rightarrow f(x)=f(y)$.
Let $I$ a compact set and $f\in\mathcal{C}([0,1]^I)$. Then exists $J\subset I$, countable or finite, such that:
if $x,y\in [0,1]^I$ such that $x\big|_J=y\big|_J\Rightarrow f(x)=f(y)$.