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 ==
* If ''P'' is a complete upper semilattice, the Lawson topology on ''P'' is always a complete T<sub>1</sub> 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. {{isbn|0-521-80338-1}}
== External links == *"[http://www.entcs.org/files/mfps19/83011.pdf How Do Domains Model Topologies?]," Paweł Waszkiewicz, Electronic Notes in Theoretical Computer Science 83 (2004)
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Category:Domain theory Category:General topology Category:Order theory