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Answer by Matthew C for Counter example of continous function such that there...
This may be overkill, but the cantor function with $S=$ the middle-thirds cantor set will work:2 properties of this function are: $S^\circ = \emptyset$ and $f(S)=[0,1]$
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$S^\circ$ 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...
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