Darboux calculus

Marco Aldi; Alexander McCleary

doi:10.2140/involve.2019.12.361

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.

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Marco Aldi. Alexander McCleary. "Darboux calculus." Involve 12 (3) 361 - 380, 2019. https://doi.org/10.2140/involve.2019.12.361

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Received: 6 May 2016; Revised: 20 December 2017; Accepted: 22 May 2018; Published: 2019

First available in Project Euclid: 5 February 2019

zbMATH: 07033136

MathSciNet: MR3905335

Digital Object Identifier: 10.2140/involve.2019.12.361

Subjects:

Primary: 06A06 , 06A11 , 18B35 , 26A06 , 97I10

Keywords: foundations of real analysis , Kan extensions , partially ordered sets

Abstract

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