n-anti-exchange closure operators (Q579287)

The notion of an anti-exchange closure operator generalizes the order ideal closure of a partially ordered set. The aim of this paper is to characterize generating sets with respect to a closure operator not necessarily anti-exchange. For this purpose there are considered for cardinal numbers n so-called n-anti-exchange closure operators where for each set Y with cardinality \(n+1\) there exist certain closed Z such that \(Y\setminus Z\) is smaller than \(n+1\). There is given a generalization of the connection between anti-exchange closure operators and subsets of isolated elements for n-anti-exchange closure operators and systems \(X_ n\).