Topological difference posets
Vladimír Palko · Czech digital mathematics library · 1997
Difference posets (D-posets) are partially ordered sets with a par tial difference operation.Special cases of D-posets are orthomodular posets or systems of fuzzy sets.In this paper, we define a topological D-poset as a D-poset with a topology guaranteeing the continuity of the difference operation, and a topological lattice D-poset as a lattice D-poset with a topology guaranteeing the continuity of the difference operation and lattice operations.If these topologies are uniform and the operations are uniformly continuous, we speak of uniform D-posets and uniform lattice D-posets.In the paper, several examples of uniform D-posets are exhibited.The main result is the theorem asserting that the topo logical completion of a uniform Hausdorff lattice D-poset in which all monotone nets are Cauchy is also a uniform Hausdorff lattice D-poset, which is a complete lattice.This is the generalization of a known result for orthomodular lattices ([14])-AMS Subject Classification (1991): Primary 06B30, 54F05.