PomeDefinition 17.15.25.FA768FFB9E17 Let $(\Gamma ^ i)_{i\in I}$ be a non-empty family in $\mathrm{TC}(X,\theta )_{>0}$ satisfying (17.15.21). Let $\operatorname{Fin}(I)$ denote the net of non-empty finite subsets of $I$, ordered by inclusion. Then we define
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17.15.26
\begin{equation} \operatorname *{sup}_{i\in I}{}\! {}^{*}\Gamma ^ i\coloneqq \operatorname *{sup}_{J\in \operatorname{Fin}(I)}{}\! {}^{*} \left( \bigvee _{j\in J} \Gamma ^ j\right). \end{equation}
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