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#REDIRECT [[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>{{cite web|url=http://www.PaulTaylor.EU/ASD |title=Paul Taylor's site |publisher=Paultaylor.eu |date= |accessdate=2013-09-23}}</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 [[infinitesimal]]s and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains.
*[[Constructive analysis]], which is built upon a foundation of [[constructive logic|constructive]], rather than classical, logic and set theory.
*[[Intuitionistic analysis]], which is developed from constructive logic like constructive analysis but also incorporates [[choice sequence]]s.
*[[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.
[[Non-standard analysis]] and the calculus it involves, [[non-standard calculus]], are considered part of [[classical mathematics]] (i.e. The concept of "[[hyperreal number]]" it uses, can be constructed in the framework of [[Zermelo–Fraenkel set theory]]).
[[Multiplicative calculus|Non-Newtonian calculus]] is also a part of [[classical mathematics]].
==References==
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{{DEFAULTSORT:Non-Classical Analysis}}
[[Category:Non-classical analysis]]
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