Lawson topology

In mathematics and theoretical computer science, the Lawson topology, named after Jimmie D. Lawson, is a topology on partially ordered sets (posets) 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

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

## See also

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* Formal ball

## References

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* 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. ISBN 0-521-80338-1

## External links

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

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