Non-classical analysis: Difference between revisions

Revision as of 07:52, 23 September 2013

Revision as of 07:53, 23 September 2013

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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,<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 [[infinitesimals]] 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.