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Auxiliary relations and sandwich theorems God, Chris Jung, Achim Knight, Robin Kopperman, Ralph Adjoint auxiliary relation continuous poset pairwise completely regular (and pairwise normal) bitopological space upper (lower) semicontinuous Urysohn relation A well-known topological theorem due to Kat\v etov states: Suppose $(X,\tau)$ is a normal topological space, and let $f:X\to[0,1]$ be upper semicontinuous, $g:X\to[0,1]$ be lower semicontinuous, and $f\leq g$. Then there is a continuous $h:X\to[0,1]$ such that $f\leq h\leq g$. We show a version of this theorem for many posets with auxiliary relations. In particular, if $P$ is a Scott domain and $f,g:P\to[0,1]$ are such that $f\leq g$, and $f$ is lower continuous and $g$ Scott continuous, then for some $h$, $f\leq h\leq g$ and $h$ is both Scott and lower continuous. As a result, each Scott continuous function from $P$ to $[0,1]$, is the sup of the functions below it which are both Scott and lower continuous. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Chris God and Achim Jung and Robin Knight and Ralph Kopperman 2005 Is Part Of Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.04351.8 urn:nbn:de:0030-drops-1348 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.8 eng https://creativecommons.org/licenses/by/4.0/legalcode