Involve: A Journal of Mathematics
- Volume 12, Number 3 (2019), 361-380.
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.
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
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