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If $X$ is a normal space having disjoint closed subspaces $A$ and $B$, is there a continuous function $f:X \to [0,1]$ such that ${f^{ - 1}}(0) = A$ and ${f^{ - 1}}(1) = B$? (We have already known there is a $f$ such that $f(A) = 0$ and $f(B) = 1$ )

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