Being a proper trapezoid ordered set is a comparability invariant

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Authors	NIEDERLE Josef
Year of publication	2000
Type	Article in Periodical
Magazine / Source	Order
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	autonomous subset; comparability invariant; interval ordered set; proper interval dimension; trapezoid ordered set
Description	It is proved that if we replace an autonomous subset of a finite proper trapezoid ordered set with a proper trapezoid ordered set, then we obtain a proper trapezoid ordered set provided the autonomous subset is not an antichain, and analogously in the \(k\)-dimensional case. As corollaries we obtain that being a proper trapezoid ordered set is a comparability invariant, more generally, proper interval dimension is a comparability invariant.
Related projects:	Categorical methods of the theory of structures and computer science