Definition:Way Below Open

Definition

Let $\left({S, \preceq}\right)$ a preordered set.

Let $X$ be a subset of $S$.

Then $X$ is way below open if and only if:

$\forall x \in X: \exists y \in X: y \ll x$

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_6:def 1