Lawson topology explained

In mathematics and theoretical computer science the Lawson topology, named after Jimmie D. Lawson, is a topology on partially ordered sets used in the study of domain theory. The lower topology on a poset P is generated by the subbasis consisting of all complements of principal filters on P. The Lawson topology on P is the smallest common refinement of the lower topology and the Scott topology on P.

Properties

• If P is a complete upper semilattice, the Lawson topology on P is always a complete T₁ topology.

See also

• Formal ball

References

• G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott (2003), Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications, Cambridge University Press.

External links

• "How Do Domains Model Topologies?," Paweł Waszkiewicz, Electronic Notes in Theoretical Computer Science 83 (2004)