A type of topological spaces whose notion
of continuity is equivalent to continuity in ωCPOs.
x is an ω-Sup of a chain c if it is the least upper bound of the range of c.
The characteristic function of open sets is monotone and preserves
the limits of chains.
A Scott topological space is defined on preorders
such that their open sets, seen as a function α → Prop,
preserves the joins of ω-chains
α → Prop
not_below is an open set in Scott α used
to prove the monotonicity of continuous functions