$S^\circ$ denotes the interior of a set $S$. Is there an example of a continuous function $f$ and a set S with $(f(X))^\circ \not\subset f(S^\circ)$ ?
I know that$f(S^\circ)\subset (f(S))^\circ$ is not always true; for example
I tried hard but I could not find counterexample for $(f(S))^\circ\subset f(S^\circ)$
Any help will be appreciated