Definition:Compact Element

Definition

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

Let $x \in S$.

Then $x$ is compact (element) if and only if $x \ll x$

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_3:def 2