partially ordered set

English

Wikipedia

A partially ordered set with divisibility relation

Noun

partially ordered set (plural partially ordered sets)

1. (set theory) A set having a specified partial order.
2. (set theory) Said set together with said partial order; the ordered pair of said set and said partial order.

Usage notes

• The two senses are commonly used interchangeably, there rarely being a need to distinguish between the two entities.

Synonyms

• poset
• See also Wikisaurus:partially ordered set

Hyponyms

• lattice
• totally ordered set

Translations

set having a specified partial order

• Czech: uspořádaná množina (cs) f

• Japanese: 半順序集合 (ja) (はんじゅんじょしゅうごう, hanjunjo-shūgō)