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Let $S,T$ be sets and let $\Lambda$ be an index-set. Let $f:S\to T$ and $\{A_\lambda\}_{\lambda\in\Lambda}$ be a collection of subsets in $S$ (i.e. $A\lambda\subset S$ for all $\lambda\in\Lambda$). Does $f$ satisfy $$f\left[\bigcap_{\lambda\in\Lambda} A_\lambda\right]\subset\bigcap_{\lambda\in\Lambda} f[A_\lambda]\text{ and }f\left[\bigcup_{\lambda\in\Lambda} A_\lambda\right]=\bigcup_{\lambda\in\Lambda} f[A_\lambda]?$$

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    yes, it is true2012-07-13
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    Note that in the first, we need not have equality.2012-07-13
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    That's strange. Someone downvoted all the posts on this page.2013-05-18

3 Answers 3