Non-classical analysis: Difference between revisions

Revision as of 16:10, 17 June 2006

Revision as of 03:57, 7 July 2006

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Such systems include:

*[[non-standard analysis]]

*[[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.

*[[smooth infinitesimal analysis]]

*[[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.

*[[constructivistConstructivist analysis]], (analysiswhich 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 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]]

*[[constructivist analysis]] (analysis built upon a foundation of [[constructivist logic|constructivist]], rather than classical, logic and set theory)

*[[paraconsistentParaconsistent analysis]], (analysiswhich 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.

[[Category:Mathematical analysis]]