Autor(en)
Lihova, J
Titel
On posets with isomorphic interval posets
Teil von
• Czechoslovak mathematical journal, 1999-03, Vol.49 (1), p.67-80
Ort / Verlag
New York: Kluwer Academic Publishers-Plenum Publishers
Quelle
Beschreibungen
Let $$\mathbb{A} = (A, \leqslant )$$ be a partially ordered set, Int $$\mathbb{A}$$ the system of all (nonempty) intervals of $$\mathbb{A},$$ partially ordered by the set-theoretical inclusion $$\subseteq$$ . We are interested in partially ordered sets $$\mathbb{B} = (B, \leqslant )$$ with Int $$\mathbb{B}$$ isomorphic to Int $$\mathbb{A}$$ . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If $$\mathbb{A}$$ is a directed partially ordered set, the only $$\mathbb{B}$$ with Int $$\mathbb{B}$$ isomorphic to Int $$\mathbb{A}$$ are $$\mathbb{A}_1^\delta \times \mathbb{A}_2$$ corresponding to direct decompositions $$\mathbb{A}_1 \times \mathbb{A}_2$$ of $$\mathbb{A}$$ ( $$\mathbb{A}_1^\delta$$ denotes the dual of $$\mathbb{A}_1$$ . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].
Format
Sprache(n)
Englisch
Identifikator(en)
ISSN: 0011-4642
ISSN: 1572-9141
DOI: 10.1023/A

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