PomeProposition 21.11.36.7A76E56311F5 Let $\{ F_ i\} _{i\in I}$ be a non-empty family in $\mathrm{Conv}^{\mathrm{prop}}(N)$. Then
\[ \left(\bigwedge _{i\in I} F_ i\right)^*=\bigvee _{i\in I} F_ i^*,\quad \left(\bigvee _{i\in I} \operatorname{cl}F_ i\right)^*=\operatorname{cl}\bigwedge _{i\in I} F_ i^*. \]
If $I$ is finite and $\overline{\operatorname{Dom}F_ i}$ is independent of the choice of $i\in I$, then
\[ \left(\bigvee _{i\in I} F_ i\right)^*=\bigwedge _{i\in I} F_ i^*. \]
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