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

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.


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