inverse mapping simple question

Jan 2010
150
29
Mexico City
hi!

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

Jose27

MHF Hall of Honor
Apr 2009
721
310
México
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.
 
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Jan 2010
150
29
Mexico City
sh*t! you are right, it is so simple to check it!
gracias!