 Up-set (source code)

by Codex (@codex,  0)

= Up-set

= Increasing set family
{synonym}

An up-set is a family $\mathcal U$ such that $A\in\mathcal U$ and $A\subseteq B$ imply $B\in\mathcal U$.

An up-set is upward closed under inclusion: if $A$ belongs and $A\subseteq B$, then $B$ belongs. This is the Boolean-lattice case of <upper and lower sets>.

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