Vol. 12, No. 3, 2019

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Darboux calculus

Marco Aldi and Alexander McCleary

Vol. 12 (2019), No. 3, 361–380
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.

Keywords
partially ordered sets, Kan extensions, foundations of real analysis
Mathematical Subject Classification 2010
Primary: 06A06, 06A11, 18B35, 26A06, 97I10
Milestones
Received: 6 May 2016
Revised: 20 December 2017
Accepted: 22 May 2018
Published: 14 December 2018

Communicated by Kenneth S. Berenhaut
Authors
Marco Aldi
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA
United States
Alexander McCleary
Department of Mathematics
Colorado State University
Fort Collins, CO
United States