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| *], a recent theory of general topology founded on the ] of locally compact locales. It allows the development of a form of constructive real analysis by topological means. | *], a recent theory of general topology founded on the ] of locally compact locales. It allows the development of a form of constructive real analysis by topological means. | ||
| *], a recent development of geometric integration theory which incorporates ]and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains. | *], a recent development of geometric integration theory which incorporates ] and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains. | ||
| *], which is built upon a foundation of ], rather than classical, logic and set theory. | *], which is built upon a foundation of ], rather than classical, logic and set theory. | ||
Revision as of 03:58, 7 July 2006
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.
- 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.