#REDIRECT [[ Category:Mathematical analysis #Other topics]] ▼
In [[mathematics]], '''non-classical analysis''' is any system of analysis, other than classical [[real analysis]], and complex, vector, tensor, etc., analysis based upon it.
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Such systems include:
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*[[Abstract Stone duality]]<ref>[http://www.PaulTaylor.EU/ASD Paul Taylor's site]</ref>, a programme to re-axiomatise [[general topology]] ''directly'', instead of using [[set theory]]. It is formulated in the style of [[type theory]] and is in principle computable. It is currently able to characterise the [[category (mathematics)|category]] of (not necessarily Hausdorff) computably based locally compact spaces. It allows the development of a form of constructive real analysis using topological rather 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.
*[[Constructivist analysis]], which is built upon a foundation of [[constructivist logic|constructivist]], rather than classical, logic and set theory.
*[[Intuitionistic analysis]], which is developed from constructivist logic like constructivist analysis but also incorporates [[choice sequence]]s.
*[[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 logic|paraconsistent]], rather than classical, logic and set theory.
*[[Smooth infinitesimal analysis]], which is developed in a smooth topos.
==Notes==
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▲[[Category:Mathematical analysis]]
[[Category:Mathematical logic]]
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