after the lifting $\tilde f$ of $f$ is defined, the book goes on to prove its continuity. And in that part, the book says that replacing $U$ by a smaller neighborhood, $V_0$ can be contained in $N$. But why is it possible? How to construct a smaller neighborhood such that $V_0$ can be contained in $N$?
2026-05-05 20:04:06.1778011446
A question about the proof of general lifting theorem in Munkres topology p.479
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