Version française

Cahiers du Centre de Logique, vol. 12

References

Paul van Praag (éditeur), Aspects de la dualité en mathématique
volume 12 of the Cahiers du Centre de logique, Academia-Bruylant, Louvain-la-Neuve (Belgium), 2002, +/-80 pages
ISBN 2-8729-687-6

Summary

This volume contains four papers that were contributed to the "Groupe de Contact" on duality in mathematics, held in 2001 at the "Université de Mons-Hainaut".

Karine Chemla and Serge Pahaut show that among the sources of duality in mathematics there was the observation, made by Gergonne, that one obtains new theorems if the terms " angle " and " side " are exchanged in the Euler's sentences about spherical triangles.

Francis Buekenhout surveys the history from the opposition between Gergonne and Poncelet to the classicals groups and the theory of Tits buildings.

Maurice Boffa investigates the role of the continuum hypothesis in the duality of sets of real numbers of measure zero and the meager sets.

Francis Borceux shows that category theory is a particularly suitable setting for a general approach to duality; he establishes with various examples the natural and fruitful character of the concept of dual category of a given category.

Table of contents

Chemla, K. Pahaut, S.	Histoire ou préhistoire de la dualité. Relectures des triangles sphériques avec et après Euler
Buekenhout, Fr.	La dualité en géométrie projective
Boffa, M.	Théorie des ensembles et dualité
Borceux, Fr.	La dualité gauche-droite en théorie des catégories
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October 23, 2015