Non-classical analysis

In mathematics, non-classical analysis is any system of analysis, other than classical real analysis, and complex, vector, tensor, etc., analysis based upon it.

Such systems include:

• 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.

• Constructivist analysis, which is built upon a foundation of constructivist, rather than classical, logic and set theory.

• 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.

• p-adic analysis

• Paraconsistent analysis, which is built upon a foundation of paraconsistent, rather than classical, logic and set theory.

• Smooth infinitesimal analysis, which is developed in a smooth topos.