# If the closures of two subsets of a topological space are equal, are the closures of the images of the two subsets under a continuous map also equal?

Suppose $A$ and also $B$ are parts of a topological room $X$ such that $\newcommand{cl}{\operatorname{cl}}\cl(A) = \cl(B)$.

Allow $f\colon X\to Y$ be a continual map of topological rooms.

Does that mean that $\cl(f(A)) = \cl(f(B))$?

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2022-07-25 20:46:59
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