I've been struggling with providing examples of the following:
1) A continuous function $f$ and a connected set $E$ such that $f^{-1}(E)$ is not connected
2) A continuous function $g$ and a compact set $K$ such that $f^{-1}(K)$ is not compact
I've been struggling with providing examples of the following:
1) A continuous function $f$ and a connected set $E$ such that $f^{-1}(E)$ is not connected
2) A continuous function $g$ and a compact set $K$ such that $f^{-1}(K)$ is not compact