Question related to continuity in Topology ( A proof i am unable to understand)

That is the step that actually uses the hypothesis (c). In (c) take $A$ to be $f^{-1}[B]$; we’re assuming that $p\in\operatorname{cl}A$, so by (c) we have $f(p)\in\operatorname{cl}f[A]=\operatorname{cl}f\big[f^{-1}[B]\big]$.

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General Topology

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