As everyone knows, one popular notion of Scott domain is defined as a bounded complete algebraic cpo. These are closely related to algebraic lattices: (i) A Scott domain becomes an algebraic lattice with the adjunction of an (isolated) top element. (ii) Every non-empty Scott-closed subset of an algebraic lattice is a Scott domain. Moreover, the isolated (= compact) elements of an algebraic latt...

A semilattice decomposition of an inverse semigroup has good internal mapping properties. These are used to give natural proofs of some embedding theorems, which were originally proved in a rather artificial way. The reader is referred to [1] for the basic theory of inverse semigroups. In an earlier paper [3] we proved the following embedding result: (1) An E-unitary inverse semigroup is isomor...

Abstract For a Hausdorff topologized semilattice X its Lawson number $$\bar{\Lambda }(X)$$ Λ ¯ ( X ) is the smallest cardinal $$\kappa $$ κ such that for any distinct points $$x...