inverse mapping simple question

**mabruka** · May 9th 2010, 02:41 PM

hi!

Does the property
$<br /> f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)<br />$
hold for an infinite union of sets??

**Jose27** · May 9th 2010, 03:08 PM

Originally Posted by mabruka

hi!

Does the property
$<br /> f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)<br />$
hold for an infinite union of sets??

Why wouldn't it? It's easy to check that $\{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \}$ which is equivalent to your statement.

**mabruka** · May 9th 2010, 03:12 PM

sh*t! you are right, it is so simple to check it!
gracias!

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