Recursive Quantum Functions, Avoidable Points, & Shadow Points in Recursive Analysis

In this paper we summarize our approach and findings in a point-free setting for recursive topology and recursive analysis. Recursive analysis has received intensive attention recently and our approach, while differing from those of other schools, does have connections to them. Here, we also present some of our findings on quantum and total recursive functions on the reals, introduce our classification of nonrecursive points, and remark on the connections between our work and the works of others.