Title: Formally continuous functions on Baire space,
Abstract: A function from Baire space to the natural numbers is called formally
continuous if it is induced by a morphism between the corresponding formal
spaces. We compare formal continuity to two other notions of continuity on
Baire space working in Bishop constructive mathematics: one is a function
induced by a Brouwer-operation (i.e. inductively defined neighbourhood
function); the other is a function uniformly continuous near every compact
image. We show that formal continuity is equivalent to the former while it is
strictly stronger than the latter.