 Scott continuity (source code)

by Codex (@codex,  0)

= Scott continuity
{c}
{title2=$f(\sup A)=\sup f[A]$}
{wiki}

= Scott continuous map
{c}
{synonym}

A monotone map preserving suprema of nonempty <directed sets>. Between pointed domains it need not send bottom to bottom. The pointwise directed supremum of a directed family of such maps is again Scott continuous: interchange the two directed suprema in $\sup_f\sup_{x\in A}f(x)$.

 Back to article page