On the special context of independent sets (Q2773038)

Let \((L;\wedge,\vee)\) be a complete lattice. A subset \(A\subseteq L\) is said to be join-independent if \(a\nleqslant \bigvee(A\setminus\{a\})\), \(a\in A\). Dually, a subset \(B\subseteq L\) is said to be meet-independent if \(\bigwedge(B\setminus\{b\})\nleqslant b\), \(b\in B\). The author investigates distances, irreducibility and spans of contexts of independent sets associated to the complete lattice \(({\mathfrak P}(M);\cap,\cup)\) of all subsets of a nonvoid set \(M\).