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Darboux calculus

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2019Embargo end date: 01 Jan 2016 English Publisher:Mathematical Sciences PublishersJournal:Involve, a Journal of Mathematics, volume 12, pages 361-380 (issn: 1944-4176, eissn: 1944-4184, Copyright policy )
Authors: Aldi, Marco; McCleary, Alexander;

doi: 10.2140/involve.2019.12.361 , 10.48550/arxiv.1605.01811

arXiv: 1605.01811

Darboux calculus

Abstract

We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including Dedekind cuts, limits and continuity.

18 pages, exposition improved

Related Organizations
Keywords

partially ordered sets, Kan extensions, Foundations: limits and generalizations, elementary topology of the line, Mathematics - Category Theory, 97I10, 18B35, One-variable calculus, 26A06, Partial orders, general, 06A06, Mathematics - Classical Analysis and ODEs, foundations of real analysis, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Category Theory (math.CT), 06A11

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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