Suppose I have a continuous function $f : X \rightarrow Y$ of topological spaces $X $ and $Y$. If I have two sets $U$ and $V$ in $X$ such that the image under $f$ of both of these sets is the same $f(U) = f(V) $ and $U$ is open- would $V$ have to be open?
sets with same image under continuous map
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general-topology
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0The rain in Spain stays mainly in the plain. – 2012-12-01
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0How about if $f(U) $ is open? – 2012-12-01
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0Andre deleted his comment about rain. http://www.youtube.com/watch?v=uVmU3iANbgk – 2012-12-01
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0see edit. =-=-=-=-=-=-=-=-=-=-= – 2012-12-01