… poset to obtain the \({{\mathcal {Z}}}\)-completion. In Sect. 1, we recall the basic facts on closure
operators … 2, we define two closure operators \(\rho _{{{\mathcal {Z}}}}\) and \(\hat{\rho }_{{{\…

… on posets to their corresponding F, I -completions. Finally, we use the previous results to
obtain adequate F, I -completions … Recall that a closure operator C on a set X is said to be …

… completion is continuous(algebraic). Using the D-completion, we construct the local dcpo-completion
of posets… In this section we recall the basic definitions and results on posets that will …

… Using closure operators we show how to form the chaincompletion P of any poset P. …
Since our emphasis is on chains, the chain-completion of a poset is more natural for us than the …

… , we mean by a core quasiorder on a set P an idempotent relation ρ on P such that each of
… ) is Z-ary and Z-precomplete then X is the -ideal completion Z P and Z is its closure operator. …

… Although the extensions of unary operators need not be operators on the completions,
we show that the extensions of unary residuated maps are residuated. We also investigate …

… A closure operator\(\rho _{X}\) on X is a function from the power set \(2^{X}\) to itself such that
\… If Z is a subset system on POSET and X is a closure space, we denote the family of subsets …

… In particular, we focus on partially ordered sets (posets) and on occurrence nets, the
basic model in net theory for modelling non-sequential processes (see [16] and [7]). …

… The completions that we focus on here are called 1-completions and … completion of P gives
rise to closure operators (given by the composition of the two Galois maps in each case) on U(…

… In Theorem 4.1 we compute the spectrum of the operator UD … Many of our results on
differential posets are new even for … Thus KS is the completion of KS in a suitable topology. Given …