On some properties of mappings of sheafspaces

The note is a sequel to [1], [2]. It is proved that the domains of constructive mappings of sheaf-spaces are intersections of enumerable families of constructively open sets (and under some additional conditions even intersections of enumerable families of Lacombe sets). An approximative type notion of neighbourhood operator is introduced and a relation between the neighbourhood operators and constructive mappings is established. Two theorems on anormal form of constructive operators of finite types are formulated.