Lawson topology

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In mathematics and theoretical computer science the Lawson topology, named after J. 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.


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

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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

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