*[[http://www.PaulTaylor.EU/ASD Abstract Stone duality]], a recentprogramme theoryto ofre-axiomatise [[general topology]] ''directly'', instead of using [[set theory]]. It is foundedformulated onin the style of [[topostype theory]] and is in principle computable. It is currently able to characterise the [[category (mathematics)|category]] of (not necessarily Hausdorff) computably based locally compact localesspaces. It allows the development of a form of constructive real analysis byusing topological meansrather than [[Cauchy sequence|metrical]] arguments.
*[[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.
