Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 3 (2019), 361-380.

Darboux calculus

Marco Aldi and Alexander McCleary

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Involve, Volume 12, Number 3 (2019), 361-380.

Received: 6 May 2016
Revised: 20 December 2017
Accepted: 22 May 2018
First available in Project Euclid: 5 February 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 06A06: Partial order, general 06A11: Algebraic aspects of posets 18B35: Preorders, orders and lattices (viewed as categories) [See also 06-XX] 26A06: One-variable calculus 97I10: Comprehensive works

partially ordered sets Kan extensions foundations of real analysis


Aldi, Marco; McCleary, Alexander. Darboux calculus. Involve 12 (2019), no. 3, 361--380. doi:10.2140/involve.2019.12.361.

Export citation


  • A. Edalat and A. Lieutier, “Domain theory and differential calculus (functions of one variable)”, Math. Structures Comput. Sci. 14:6 (2004), 771–802.
  • L. Fuchs, Partially ordered algebraic systems, Pergamon, Oxford, 1963.
  • S. Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer, 1971.
  • W. Rudin, Principles of mathematical analysis, McGraw-Hill, New York, 1953.
  • P. Taylor, Practical foundations of mathematics, Cambridge Studies in Advanced Math. 59, Cambridge Univ. Press, 1999.
  • P. Taylor, “A lambda calculus for real analysis”, J. Log. Anal. 2 (2010), art. id. 5.
  • The Univalent Foundations Program, Homotopy type theory: univalent foundations of mathematics, Inst. Advanced Study, Princeton, NJ, 2013.