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Could someone please clarify the following to me?

Suppose $f:X\to Y$ is a surjection from a topological space, $X$, to some set, $Y$. Then is it necessarily true that $f^{-1}(\emptyset)=\emptyset$?

I think this is true, but I want to be sure. Thank you.

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    @Jonathan: Thank you again! That is very well explained.2012-05-05

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Which points (wherever you want) are mapped to the null set? None. This is right.

To be more precise: if there was a point whose image was in the empty set, then the empty set wouldn't be empty.