# Characterization of posets of intervals

Archivum Mathematicum (2000)

- Volume: 036, Issue: 3, page 171-181
- ISSN: 0044-8753

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topLihová, Judita. "Characterization of posets of intervals." Archivum Mathematicum 036.3 (2000): 171-181. <http://eudml.org/doc/248538>.

@article{Lihová2000,

abstract = {If $A$ is a class of partially ordered sets, let $P(A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A\in A.$ We give an algebraic characterization of elements of $P(A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a\in A$ there exist a minimal element $u$ and a maximal element $v$ with $u\le a\le v,$ respectively.},

author = {Lihová, Judita},

journal = {Archivum Mathematicum},

keywords = {partially ordered set; interval; partially ordered set; interval of a partially ordered set; interval poset},

language = {eng},

number = {3},

pages = {171-181},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Characterization of posets of intervals},

url = {http://eudml.org/doc/248538},

volume = {036},

year = {2000},

}

TY - JOUR

AU - Lihová, Judita

TI - Characterization of posets of intervals

JO - Archivum Mathematicum

PY - 2000

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 036

IS - 3

SP - 171

EP - 181

AB - If $A$ is a class of partially ordered sets, let $P(A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A\in A.$ We give an algebraic characterization of elements of $P(A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a\in A$ there exist a minimal element $u$ and a maximal element $v$ with $u\le a\le v,$ respectively.

LA - eng

KW - partially ordered set; interval; partially ordered set; interval of a partially ordered set; interval poset

UR - http://eudml.org/doc/248538

ER -

## References

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