Normal functors and hereditary paranormality

A topological space is said to be paranormal if every countable discrete collection of closed sets {Dn:n<ω} can be expanded to a locally finite collection of open sets {Un:n<ω}, i.e. Dn⊂Un, and Dm∩Un≠∅ iff Dm=Dn. It is proved that if F is a normal functor F:Comp→Comp of degree ≥3 and the space F(X)∖X is hereditarily paranormal, then the compact space X is metrizable.