hi! Does the property $\displaystyle f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B) $ hold for an infinite union of sets??
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Originally Posted by mabruka hi! Does the property $\displaystyle f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B) $ hold for an infinite union of sets?? Why wouldn't it? It's easy to check that $\displaystyle \{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \}$ which is equivalent to your statement.
sh*t! you are right, it is so simple to check it! gracias!
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