theorem :: WAYBEL17:27

for S, T being complete Scott TopLattice
for f being Function of S,T st S is algebraic & T is algebraic holds
( f is continuous iff for x being Element of S
for k being Element of T st k in the carrier of (CompactSublatt T) holds
( k <= f . x iff ex j being Element of S st
( j in the carrier of (CompactSublatt S) & j <= x & k <= f . j ) ) )