Topology/Space of Recursive Algebraic Datatypes
It is possible to construct recursive datatypes (algebraic datatypes are a special case) in a suitable category of complete metric spaces, see for instance P. America and J. Rutten's Solving Reflexive Domain Equations in a Category of Complete Metric Spaces, Journal of Computer and System Sciences 39, 343-375 (1989).

As for making vector spaces out of algebraic datatypes, I do not really know, but if you explain what you want them for, we might be able to suggest something.