Definition:Compact Closure

Definition

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

Let $x \in S$.

Then compact closure of $x$, denoted $x^{\mathrm{compact}}$, is defined by

$x^{\mathrm{compact}} := \leftset {y \in S: y \preceq x \land y}$ is compact$\rightset{}$

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_8:def 2