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edit approved Oct 23, 2020 at 17:54
RobPratt
edit approved Oct 23, 2020 at 17:54
RobPratt
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Strahinja Popovic
Strahinja Popovic
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Set of upperlower bounds in poset is defined like $ A^u = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$$ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.

Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?

Set of upper bounds in poset is defined like $ A^u = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.

Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?

Set of lower bounds in poset is defined like $ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.

Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?

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Strahinja Popovic
Strahinja Popovic
  • 123
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Name for union of upsets/downsets

Set of upper bounds in poset is defined like $ A^u = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.

Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?