Interval dimension and MacNeille completion |
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| Authors: | Michel Habib Michel Morvan Maurice Pouzet Jean-Xavier Rampon |
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| Affiliation: | (1) Dépt. Informatique Fondamentale, LIRMM, CNRS et Université Montpellier II, 161 rue Ada, 34392 Montpellier, Cedex 5, France;(2) LIP, ENS Lyon, CNRS URA 1398, 46 allée d'Italie, 69364 Lyon Cedex 07, France;(3) Groupe LMDI, Institut de Mathématiques-Informatique, Université Claude-Bernard, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France;(4) IRISA, Université de Rennes I, campus de Beaulieu, 35042 Rennes Cedex, France |
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| Abstract: | Equality between the interval dimensions of a poset and its MacNeille completion, announced in [7], has been obtained by the authors as a byproduct of their study of Galois lattices in [8]. The purpose of this note is to give a direct proof, similar to the classical proof of Baker's result stating that the dimension (in the Dushnik-Miller sense) of a poset and its MacNeille completion are the same.Supported by French PRC Math-Info. |
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| Keywords: | 06A07 |
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