Let $C(E,F)$ be the set of continouos maps between metric spaces $E$ and $F$. Suppose we are given the $C^0$ fine topology and a metric topology on $C(E,F)$. We know that the fine topology is finer than the compact-open topology, but is it finer than metric topology?
2026-04-19 17:37:49.1776620269
Is the $C^0$-fine topology finer than the metric topology?
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