Abstract Stone Duality , a recent theory of general topology founded on the Topos of locally compact locales. It allows the development of a form of constructive real analysis by topological means.
Chainlet Geometry , a recent development of geometric integration theory which incorporates Infinitesimals and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains.
Intuitionistic Analysis , which is developed from constructivist logic like constructivist analysis but also incorporates choice sequences.
Non-standard Analysis , develops rigorous infinitesmals within a new number system along with a transfer principle allowing them to be applied back to the real numbers.
