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- W30235522 abstract "A well-known topological theorem due to Katv etov states:Suppose $(X,tau)$ is a normal topological space, and let $f:Xto[0,1]$ be upper semicontinuous, $g:Xto[0,1]$ be lower semicontinuous, and $fleq g$. Then there is a continuous $h:Xto[0,1]$ such that $fleq hleq g$.We show a version of this theorem for many posets with auxiliary relations. In particular, if $P$ is a Scott domain and $f,g:Pto[0,1]$ are such that $fleq g$, and $f$ is lower continuous and $g$ Scott continuous, then for some $h$, $fleq hleq g$ 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." @default.
- W30235522 created "2016-06-24" @default.
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- W30235522 date "2005-01-01" @default.
- W30235522 modified "2023-09-24" @default.
- W30235522 title "Auxiliary relations and sandwich theorems." @default.
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