Let f: (S,d_s) -> (T,d_t) be a function.
Show that f is continuous on S iff f^(-1)(int B) is contained in
int ( f^{-1}(B) ) for any B < T. Also, show that f is continuous
on S iff f(cl(A)) is contained in cl(f(A)) for any A < S.
(< means subset).
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