Axiom:Axiom of Approximation

Definition

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

The axiom of approximation says

$\forall x \in S: x = \map \sup {x^\ll}$

where $x^\ll$ denotes the way below closure of $x$.

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 5