Question

real analysis
will post with editor

Answer 1

\[f:\Omega\rightarrow\Phi,A\subset\Omega,\{A_i\}_{i\in I}\space is \space an \space indexed\space collection\space of\space subsets\space of\space\Omega\\prove\\f(\large\cup_{i\in I}\space A_i)= \large\cup_{i\in I}f(A_i)\]