Definition:Scott Sigma

Definition

Let $L = \struct {S, \preceq}$ be an ordered set.

Scott sigma $\map \sigma L$ is a set of subsets of $S$ and equals to

$\leftset {U \subseteq S: U}$ is upper and has property (S)$\rightset{}$

Source of Name

This entry was named for Dana Stewart Scott.

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article WAYBEL11:def 12