Solution
= Solution
\b[False.] The constant <continuous function> $f:\mathbb R\to\mathbb R$, $f(x)=0$, sends the open set $\mathbb R$ to $\{0\}$, which is not open. Therefore continuity alone does not imply an <open map>.
= Solution
\b[False.] The constant <continuous function> $f:\mathbb R\to\mathbb R$, $f(x)=0$, sends the open set $\mathbb R$ to $\{0\}$, which is not open. Therefore continuity alone does not imply an <open map>.