### Abstract

Two general kinds of subsets of a partially ordered set P are always retracts of P: (1) every maximal chain of P is a retract; (2) in P, every isometric, spanning subset of length one with no crowns is a retract. It follows that in a partially ordered set P with the fixed point property, every maximal chain of P is complete and every isometric, spanning fence of P is finite.

Original language | English |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1980 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Duffus, D., Rival, I., & Simonovits, M. (1980). Spanning retracts of a partially ordered set.

*Discrete Mathematics*,*32*(1), 1-7. https://doi.org/10.1016/0012-365X(80)90093-X