Do you have an example of a continuous map $f\colon A\to B$ between topological spaces, such that $f$ is bijective and its inverse is not continuous?
I remark that the category must be that of topological spaces, not of haussdorf or compact ones.
2026-03-27 03:57:44.1774583864
Monic epimorphisms in topological spaces category
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Take $A$ as $\mathbb R$ endowed with the discrete topology, $B$ as $\mathbb R$ endowed with the usual topology, and $f$ as the identity map.