Connectedness Properties of Lattices
R. Vainio · Canadian Mathematical Bulletin · 1986
Abstract LetLbe a lattice andqa convergence structure (or a topology) finer than the interval topology ofL.In case of compact maximal chains and continuous lattice translations, the connected components of the space(L,q)are characterized using lattice conditions only. Moreover, lattice conditions ofLare related to connectedness conditions of the order convergence space (L,o).Throughout this note, maximal chain conditions and maximal chain techniques play an important role.