Transitive closures of binary relations. III. (English) Zbl 1158.06301

Flaška, Václav; Ježek, Jaroslav; Kepka, Tomáš

Acta Univ. Carol., Math. Phys. 49, No. 1, 25-31 (2008).

Summary: This extremely short expository note collects a few more or less notoriously known results on the covering relation \(\beta\) in lattices. Special attention is paid to the property that any two \(\beta\)-sequences connecting two given elements are of the same length. We refer to the previous parts of this series of papers [ibid. 48, No. 1, 55–69 (2007; Zbl 1135.03344); ibid. 48, No. 1, 71–80 (2007; Zbl 1135.03343)] for terminology, notation, further references, etc.

MSC:

06B05	Structure theory of lattices
03E20	Other classical set theory (including functions, relations, and set algebra)
06A06	Partial orders, general

Keywords:

length of sequences; covering relation in lattices

Citations:

Zbl 1135.03344; Zbl 1135.03343