Let $f : A \rightarrow B$, if $E$ is a family of subsets of $A$ and $E$ is a $B-algebra$ (borel algebra). My question is:
Is $f(E) = \{\ f(V) | V \in E \}$ a $B-algebra$. I suppose that this is false but how can I construct a counterexample to show it?
If someone could help me please. Thanks for your time and help.
Take $B = A$, the discrete topology in the left, the indiscrete topology in the right, $f =$ identity.