Some new closures on orders |
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Authors: | Gábor Czédli |
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Institution: | 1.Bolyai Institute,University of Szeged,Szeged,Hungary |
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Abstract: | For each of the relations “less than or equal to”, “less than”, “covered by”, and “covered by or equal to”, we characterize
finite orders (also called posets) with the property that the pair of Galois closure operators induced by the relation in
question coincides with the pair of closure operators introduced and applied in our previous paper in 2007. We also consider
the “less than or equal to” relation between the set of join-irreducible elements and the set of meet-irreducible elements,
and we show that the above-mentioned pairs of closure operators coincide for finite modular lattices. |
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Keywords: | |
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