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It’s a well-known fact that for continuous functions $f:X\to Y$ and $g:Y\to Z$ of locally connected spaces, if $g\circ f$ and $g$ are covering maps, so is $f$. I was wondering if the following statement is also true: If $g\circ f$ and $f$ are covering maps, so is $g$. I can’t find a proper counterexample and am not able to proof it. Any ideas?

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