The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications, that can be used as an effective research tool throughout mathematics and related areas.Expand

It turns out that for arbitrary subset selections Z, a poset P is strongly Z-continuous iff its Z-join ideal completion Z∨ P is Z-ary and completely distributive.Expand

A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. Using… Expand

Complete distriburivity is an old theme in lattice theory: the basic results were already proved in the early fifties by G.N. Raney. Some new features of completely distributive lattices have bet..… Expand

This work describes their patch spaces as hyperconvex and hyperregular pospaces in which every monotone net has a supremum to which it converges and provides topological generalizations of known facts for quasicontinuous posets.Expand

By a recent observation of Monjardet and Wille, a finite distributive lattice is generated by its doubly irreducible elements iff the poset of all join-irreducible elements has a distributive… Expand

We study order-theoretical, algebraic and topological aspects of compact generation in ordered sets. Today, algebraic ordered sets (a natural generalization of algebraic lattices) have their place… Expand