If $f$ is a continuous mapping from a topological space $X$ onto itself, then is there any example of $f$ such that $f^{-1}(B)$ is not bounded for a bounded set $B\in X$?
2026-03-06 03:36:15.1772768175
Boundedness of $f^{-1}(B)$ for some bounded set $B\in X$
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If $f\colon\mathbb R\longrightarrow\mathbb R$ is the null function, then $f$ is continuous and $f^{-1}\bigl(\{0\}\bigr)=\mathbb R$, which is unbounded.