Closure in general lattices
Masahiro Nakamura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1941
1. Introduction.The concept "closure" was axiomatized by F.Riesz and Kuratowski D on the field of sets, and Terasaka 2) generalized it onto abstract Boolean algebras.The object of this note is to extend it onto general lattices.Incidentally "combinations of topologies" of G. Birkhof s) are treated from more general point of view.By "closure" we mean a transformation a on a complete lattice L into itself, which satisfies [1.1] 1 aaa, 2 (a.b).a=aa,ba, 3 (aa) a=aa, 4 Oa=O.