-systems in local Noether lattices.
We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces , the corresponding partial dcpo’s of continuous real valued functions on are continuous partial dcpos; (iii) if a space is Hausdorff compact, the lattice of all S-lower semicontinuous functions on is the dcpo-completion of that of continuous real valued...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result may also...
In the present paper we deal with the existence of large homogeneous partially ordered sets having the property described in the title.