Involve: A Journal of Mathematics

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

Darboux calculus

Marco Aldi and Alexander McCleary

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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.

Article information

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

Dates
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
https://projecteuclid.org/euclid.involve/1549335627

Digital Object Identifier
doi:10.2140/involve.2019.12.361

Mathematical Reviews number (MathSciNet)
MR3905335

Zentralblatt MATH identifier
07033136

Subjects
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

Keywords
partially ordered sets Kan extensions foundations of real analysis

Citation

Aldi, Marco; McCleary, Alexander. Darboux calculus. Involve 12 (2019), no. 3, 361--380. doi:10.2140/involve.2019.12.361. https://projecteuclid.org/euclid.involve/1549335627


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References

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