Definition:Way Above Closure

Definition

Let $\left({S, \preceq}\right)$ be an ordered set.

Let $x \in S$.

The way above closure of $x$, denoted by $x^\gg$, is defined by:

$x^\gg := \left\{ {y \in S: x \ll y}\right\}$

where $\ll$ denotes the way below relation.

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 WAYBEL_3:def 4