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name for a subset of a binary relational structure which is "closed downward"?

Let $X$ be a set and suppose that $R$ is a binary relation on $X$. Suppose further that $S\subseteq X$ has the property that whenever $y\in S$ and $xRy$ ($x\in X$), then also $x\in S$. Does such an $S …
Greg Oman's user avatar