Relating Bishop's function spaces to neighbourhood spaces (Q1942042)

The author introduces into Bishop-style constructive topology the notion of a \textit{pre-function space}, as well as those of \(\Phi \)-\textit{closed} and \( \Psi \)-\textit{closed} pre-function spaces. He shows that there is an adjunction between the category of neighbourhood spaces and that of \(\Phi\)-closed pre-function spaces, and one between the category of uniform spaces (note that his notion of \textit{uniform space} is weaker than that in the constructive theory of apartness spaces) and that of \(\Psi \)-closed pre-function spaces.