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Darboux
calculus
Marco Aldi and Alexander McCleary
Vol. 12 (2019), No. 3, 361–380
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Abstract |
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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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Keywords
partially ordered sets, Kan extensions, foundations of real
analysis
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Mathematical Subject Classification 2010
Primary: 06A06, 06A11, 18B35, 26A06, 97I10
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Milestones
Received: 6 May 2016
Revised: 20 December 2017
Accepted: 22 May 2018
Published: 14 December 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Marco Aldi | |
| Department of Mathematics and
Applied Mathematics Virginia Commonwealth University Richmond, VA United States |
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| Alexander McCleary | |
| Department of Mathematics Colorado State University Fort Collins, CO United States |
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