# inverse mapping simple question

• May 9th 2010, 02:41 PM
mabruka
inverse mapping simple question
hi!

Does the property
$
f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)
$

hold for an infinite union of sets??
• May 9th 2010, 03:08 PM
Jose27
Quote:

Originally Posted by mabruka
hi!

Does the property
$
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 $\{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \}$ which is equivalent to your statement.
• May 9th 2010, 03:12 PM
mabruka
sh*t! you are right, it is so simple to check it!
gracias!